Géométrie
Triangles, cercles, géométrie analytique et démonstrations.
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read the following passage, which is modeled after an encyclopedia entr…
most major grocery stores
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calculate the area of the composite figure given below. enter the value…
38
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18. if ad = 24, db = 27, and eb = 18, find ce.
16
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read the following passage, which is modeled after an encyclopedia entr…
patted into thin circles
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ne area of the following figure and write your in the empty box. figure…
$434$
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a (a pink rectangle with length 5 cm and width 3 cm) b (a brown right -…
A. The rectangle with dimensions 3 cm and 5 cm
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8. x√2 = 19√2 · √2 19√(2·2) = 19√4 √4 √2 = (right triangle with right a…
If we follow the calculation \(19\sqrt{2}\times\sqrt{2}=19\times2 = 38\), and if we assume the equation was to find \(x\) when \(x\sqrt{2}=19\sqrt{2}\times\sqrt{2}\), then \(x = 3…
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find the missing length of the following figure if the area of the shad…
4
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graphing inequalities graph the inequality. 3. ( a geq -12 ) 4. ( x leq…
1. For $a\geq -12$: Closed circle at $-12$, shade right. 2. For $x\leq -7$: Closed circle at $-7$, shade left. 3. For $w<5$: Open circle at $5$, shade left. 4. For $d>13$: Open ci…
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a rectangle is placed around a semicircle as shown below. the width of …
\( 1.72 \) square centimeters (or \( 1.72 \, cm^2 \))
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for 16 - 17, determine whether $overleftrightarrow{jk} parallel overlef…
16. no 17. yes
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find the missing length of the following figure (the area of the figure…
4 mm.
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which of the following figure has the greate a 9 m 9 m b 6 m 10 m 10 m …
B. The trapezoid (figure B)
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find the cosine of ∠e. f 12 d 5 e simplify your answer and write it as …
\( \frac{5}{13} \)
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24. a circle is inscribed in a square so that the circle touches each s…
a. \( 5\pi \) cm
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find the sine, cosine, and tangent of ∠b. simplify your answers and wri…
\( \sin(B) = \frac{55}{73} \) \( \cos(B) = \frac{48}{73} \) \( \tan(B) = \frac{55}{48} \)
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find the area of the shaded region of the triangle giver the appropriat…
The second triangle (right triangle with legs 8 yd and 9 yd) has an area of 36 square yards, so this is the shaded region matching the given result.
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find the area of the figure given below and write your answer in the em…
$260 + 84 = 344$ $\text{cm}^2$
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the radius of a quarter circle is 4 kilometers. what is the quarter cir…
12.57 square kilometers
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the radius of a circle is 17 meters. what is the circle’s circumference…
106.81 meters
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given: \\(\\overline{ab} \\cong \\overline{cd}\\), \\(\\overline{ad} \\…
The reason for \( \overline{AF} \cong \overline{CE} \) is the **Addition Property of Congruence** (or "Segment Addition Postulate and Addition Property of Congruence") because we …
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find the area of the triangle below. be sure to include the correct uni…
$50$ square feet (or $50\ ft^2$)
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step statement reason - abcd is a parallelogram 1 (overline{bg} cong ov…
Corresponding Parts of Congruent Triangles are Congruent (CPCTC)
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find the area of the following polygon given in the first column a. a s…
a. $36\ \text{cm}^2$ b. $40\ \text{in}^2$ c. $70\ \text{ft}^2$ d. $13.5\ \text{m}^2$
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step statement reason abcd is a parallelogram bg ≅ dh given ae ≅ fc ef …
The reason for $\triangle CGE \cong \triangle AHF$ is the Side - Angle - Side (SAS) Congruence Postulate (i.e., if two sides and the included angle of one triangle are congruent t…
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step statement\treason 1\tabcd is a parallelogram \t\\overline{bg} \\co…
Alternate Interior Angles Theorem (or: If two parallel lines are cut by a transversal, then alternate interior angles are congruent)
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21. the length of a rectangular fence is 20 feet and the width is 10 fe…
c. 15 feet
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the diameter of a circle is 26 yards. what is the circle’s circumferenc…
81.68 yards
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the radius of a circle is 13 centimeters. what is the circles circumfer…
81.68 centimeters
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question given: (abcd) is a parallelogram, (overline{bg} cong overline{…
The reason for step 5 (\(AH \cong CG\)) is "Congruent segments subtracted from congruent segments form congruent segments" (since \(AD \cong BC\) and \(DH \cong BG\), so \(AD - DH…
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which shape has parallel sides and perpendicular sides? shape a shape b…
C. Shape C
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the circumference of a circle is 56.52 centimeters. what is the circles…
9.00 centimeters
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select the correct shapes. select all of the shapes that have at least …
The shapes with at least one pair of parallel sides are the orange rectangle and the yellow parallelogram.
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three shapes are shown. shape f (trapezoid), shape g (rhombus), shape h…
B. Shapes F, G, and H
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question given: abcd is a parallelogram, \\(\\overline{bg} \\cong \\ove…
For step 4, the reason is "Opposite sides of a parallelogram are congruent". To fully prove \(\overline{GE} \cong \overline{HF}\), we can continue: - Since \(\overline{AD} \cong \…
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question given: abcd is a parallelogram, \\(\\overline{bg} \\cong \\ove…
For the step where we prove \( \overline{AF} \cong \overline{CE} \), the reason is "Segment Addition Postulate and Addition Property of Congruence (or: If \( \overline{AE} \cong \…
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select the correct shapes. select all of the shapes that have at least …
The pink square, the purple right triangle. (In boxed form for the shapes: \(\boxed{\text{Pink Square}}\), \(\boxed{\text{Purple Right Triangle}}\))
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given: abcd is a parallelogram, ∠gec ≅ ∠hfa and \\(\\overline{ae} \\con…
The reason is "Angle - Side - Angle (ASA) Congruence Criterion" (or simply "ASA" as the reason for triangle congruence).
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thought provoking is the composition of a rotation and a dilation commu…
sometimes; As long as the center of dilation and the center of rotation are the same, the composition of a rotation and a dilation is commutative.
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question given: abcd is a parallelogram, ∠gec ≅ ∠hfa and \\(\\overline{…
The reason for \( \angle GCE \cong \angle FAH \) is "Alternate Interior Angles Theorem (If two parallel lines are cut by a transversal, then alternate interior angles are congruen…
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diameter: 8 yd circumference:
$8\pi$ yards (or approximately 25.12 yards)
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1 select the correct shape. which shape has a right angle?
The top - left shape (the tan - colored figure with a rectangular - like part)
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question given: abcd is a parallelogram, $\\angle gec \\cong \\angle hf…
The reason for \(BC \parallel AD\) is "Opposite sides of a parallelogram are parallel".
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13) graph the following equation. x = 7
A vertical straight line passing through the point $(7, 0)$ on the $x$-axis, extending infinitely upwards and downwards (covering all $y$-values for $x=7$).
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structure a similarity transformation maps jklm to its image pqrs. find…
1. The coordinates of point $S$ are $(6, -2)$ 2. $(x, y)\to(-2x, -2y)$
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question given: abcd is a parallelogram, ∠gec ≅ ∠hfa and \\(\\overline{…
The reason for \( \overline{AF} \cong \overline{CE} \) is the **Addition Property of Congruence** (or "If two congruent segments are added to two other congruent segments, the res…
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what is the area of this figure? 5 cm 8 cm 3 cm 15 cm 7 cm 8 cm square …
\(96\)
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given: abcd is a parallelogram and e is the midpoint of \\(\\overline{b…
The reason for \( \triangle FBE \cong \triangle DCE \) is "ASA (Angle - Side - Angle) Congruence Postulate" (or "Angle - Side - Angle congruence criterion")
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radius: 12 in circumference:
$24\pi$ inches (or approximately 75.36 inches)
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given: abcd is a parallelogram and e is the midpoint of \\(\\overline{b…
The reason for \( \angle C \cong \angle EBF \) is "Alternate interior angles are congruent (when two parallel lines are cut by a transversal)".
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given: abcd is a parallelogram and e is the midpoint of \\(\\overline{b…
The reason for \(DC \parallel AB\) is "Opposite sides of a parallelogram are parallel".
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diameter: circumference: 50.24 ft
16 ft
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l = 8.2 cm w = 4.9 cm area: perimeter:
Area: $40.18 \text{ cm}^2$ Perimeter: $26.2 \text{ cm}$
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s = 6.1 cm area: perimeter:
Area: $37.21$ cm² Perimeter: $24.4$ cm
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complete the statement of similarity based on the figures shown. quadri…
# Explanation: ## Step1: Identify the similar figure Looking at the coordinates, the blue quadrilateral (B'D'E'F') or the larger red one (B''D''E''F'')? Wait, let's check the scal…
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determine whether trapezoids defg and lmnp with the given vertices are …
no; The scale factor from $\overline{DG}$ to $\overline{LP}$ is 2, but the scale factor from $\overline{FG}$ to $\overline{NP}$ is $\frac{2}{3}$.
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there is a square with side length labeled as s. below the square, it i…
Area: $\boldsymbol{39.69}$ square centimeters Perimeter: $\boldsymbol{25.2}$ centimeters
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5 select the correct shapes. select all of the shapes that have at leas…
The orange rectangle and the green parallelogram (the second shape in the top row and the fourth shape in the bottom row) are the shapes with at least one pair of parallel sides.
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circle a has radius 1.25 cm and circle b has radius 3.75 cm. complete t…
Scale factor: $3$; Ratio of circumferences: $3$; Ratio of diameters: $3$; The two circles are similar.
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a. fill in the blanks directions: read each sentence and choose the wor…
1. consequence 2. hydroplane 3. hydrant 4. dehydrated 5. fondness 6. ambivalence 7. hydrate 8. hydraulic 9. maintenance 10. consciousness --- # Part B: True or False
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determine whether $\\triangle ghi$ and $\\triangle jkl$ with the given …
no; The scale factor from $\overline{HI}$ to $\overline{JL}$ is $\frac{2}{3}$, but the scale factor from $\overline{GH}$ to $\overline{KL}$ is $\frac{5}{6}$
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2 = (the triangle has a base of 6 ft and a height of 5 ft) area = (ther…
$15$ square feet
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given: abcd is a parallelogram and e is the midpoint of \\(\\overline{b…
Vertical angles are congruent
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4 which shape has an obtuse angle? shape a shape b shape c shape d a. s…
C. Shape B
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circle 7 cm radius = ______ diameter = ______ 7
radius = $7\ \text{cm}$ diameter = $14\ \text{cm}$
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given: abcd is a parallelogram and e is the midpoint of \\(\\overline{b…
Definition of Midpoint (A midpoint of a segment divides the segment into two congruent segments, so since \( E \) is the midpoint of \( \overline{BC} \), \( \overline{BE} \cong \o…
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3 which shape has parallel sides and perpendicular sides? shape a shape…
C. Shape C
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radius = diameter = 26
radius = 13 km diameter = 26 km
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radius = 15 diameter = 30
radius = 15 mm diameter = 30 mm
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2 select the correct answer from each dropdown menu. three shapes are s…
parallel
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a park ranger is trying to find the distance across a large pond in a n…
A = 1.15 m, B = 1.45 m, c = 13.5 m Wait, but the user's diagram has a segment labeled 1.35 m. So the dilated distance between the two points is 1.35 m, so the actual distance (c) …
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ready topic: finding the trigonometric ratios in a right triangle use t…
s: 1. \(\sin P=\frac{12}{13}\), \(\cos P=\frac{5}{13}\), \(\tan P=\frac{12}{5}\) 2. \(\sin\theta=\frac{7}{41}\), \(\cos\theta=\frac{40}{41}\), \(\tan\theta=\frac{7}{40}\) 3. \(\si…
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1 select the correct shape. which shape has a right angle?
The yellow - colored trapezoid - like shape (the first one in the top - left among the four shapes)
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radius = 5.5 diameter = 11 (there is a circle with a radius line labele…
radius = $11\ \text{m}$ diameter = $22\ \text{m}$
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a right triangle with legs 3.5 yd and 6.8 yd. find the area. area =
$11.9$ square yards
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6. complete the table. explain or show your reasoning. | object | radiu…
| object | radius | circumference | |--------------|--------------|---------------------| | clock | 7.5 cm | $15\pi$ (≈47.1 cm) | | windmill | 210 ft | $420\pi$ (≈1318.8 ft)| | bu…
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s ≠ 0 or 1; s = 1; s = -1; |s| > 1; s = 0; s < 0; 0 < |s| < 1. the imag…
To solve this, we analyze each statement based on the properties of dilation (scale factor \( s \)): ### 1. "The image and pre - image coincide (are on top of one another) and are…
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match each transformation to its scale factor description. in each case…
- A (The image is an enlargement of the pre - image) : \(|s|>1\) - B (The image is a reduction of the pre - image) : \(0 < |s|<1\) - C (The image is the same as the pre - image ro…
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a median of a triangle is a line segment with one endpoint at a vertex …
The median from \( A \) is constructed by first finding the midpoint \( M \) of \( BC \) (via perpendicular bisector construction) and then drawing segment \( AM \). Visually, it …
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an altitude of a triangle is a line segment with one endpoint at a vert…
To construct the altitude from vertex \( A \) to side \( BC \) in \( \triangle ABC \): 1. Identify side \( BC \) as the side opposite vertex \( A \). 2. Use the perpendicular cons…
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in the figure, $\\triangle xyz \\cong \\triangle mnl$. find $xy$.
8
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which angles are supplementary to each other? image of angle diagram wi…
$\angle3$ and $\angle8$
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find ( mangle 1 ). (there are two triangles, triangle ( abc ) with ( an…
\(55^\circ\)
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which angles are vertical to each other? image of intersecting lines wi…
$\angle6$ and $\angle5$
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what is the value of b? triangle with angles: 30b - 59°, 35°, and an ex…
$4.3$
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what is the value of u? 14u+22° 9u+33° 32° write your answer as an inte…
$u = 8.6$
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20. find the perimeter and area of this triangle. dimensions are in inc…
Perimeter: 30 inches, Area: 30 square inches
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what is the value of y? triangle with angles 39°, 3y - 34°, and an exte…
$21.5$
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complete the puzzle to show the sequence of locations at which you plac…
The sequence of compass point locations (red points) is: Step 1: Intersection of transversal and line a (lower red point) Step 2: Intersection of transversal and line b (middle re…
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what is the value of b? (there is a triangle with an exterior angle and…
$24$
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19. find the perimeter and area of this parallelogram. dimensions are i…
Perimeter: \( 44 \) inches, Area: \( 104 \) square inches.
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what is the value of v? there is a triangle with two angles labeled as …
$105^\circ$
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what is the value of c? there is a triangle with angles labeled as $c +…
$73$
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what is the value of v? (v - 11)° (v + 4)° (v + 41)° v = ° submit
$48$
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as a result of the construction shown, △ oae a x △ △ pjd by the sss a x…
The triangle \(\triangle OAE\cong\triangle PJD\) by the SSS triangle congruence postulate. So the first blank: \(\cong\), second blank: SSS.
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what is the value of ( b )? (there is a triangle diagram with an exteri…
$68$
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what is the value of $p$? there is a triangle and an exterior angle. on…
$87$
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scratch board unit vocab matching and word scramble use the word bank b…
1. Stylus is a hard-pointed pen-shaped instrument used for making marks or scratches into or onto a surface. 2. A Plate is often a thin, flat piece of metal or stable material use…
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what is the value of c? there is a triangle in the diagram, with one ex…
$45$
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what is $m\\angle 1$? triangle with angle 1 at top, 69° at bottom right…
$54$