Question

identify the angle pair name (corresponding, alternate interior, alternate exterior, consecutive interior, linear pair, vertical angles). circle whether they are congruent or supplementary. write the equation and solve for x. color your picture to help set up equation!!!
34.
angle pair name:
relationship: congruent/supplementary
equation:
x =
35.
angle pair name:
relationship: congruent/supplementary
equation:
x =
36.
angle pair name:
relationship: congruent/supplementary
equation:
x =
37.
angle pair name:
relationship: congruent/supplementary
equation:
x =
try these for a challenge! find the values of the variables.
38.
w =
x =
y =
z =
39.
w =
x =
y =
z =

Explanation:

Step1: Identify angle - pair for 34

These are alternate exterior angles. Alternate exterior angles are congruent.
$14x - 1=12x + 17$

Step2: Solve the equation for 34

Subtract $12x$ from both sides:
$14x-12x - 1=12x-12x + 17$
$2x-1 = 17$
Add 1 to both sides:
$2x-1 + 1=17 + 1$
$2x=18$
Divide both sides by 2:
$x=\frac{18}{2}=9$

Step3: Identify angle - pair for 35

These are alternate interior angles. Alternate interior angles are congruent.
$4x-46 = 5x - 44$

Step4: Solve the equation for 35

Subtract $4x$ from both sides:
$4x-4x-46=5x-4x - 44$
$-46=x - 44$
Add 44 to both sides:
$x=-46 + 44=-2$

Step5: Identify angle - pair for 36

These are corresponding angles. Corresponding angles are congruent.
$5x-15=x + 25$

Step6: Solve the equation for 36

Subtract $x$ from both sides:
$5x-x-15=x-x + 25$
$4x-15 = 25$
Add 15 to both sides:
$4x-15 + 15=25 + 15$
$4x=40$
Divide both sides by 4:
$x = 10$

Step7: Identify angle - pair for 37

These are vertical angles. Vertical angles are congruent.
$10x-7=8x + 5$

Step8: Solve the equation for 37

Subtract $8x$ from both sides:
$10x-8x-7=8x-8x + 5$
$2x-7 = 5$
Add 7 to both sides:
$2x-7 + 7=5 + 7$
$2x=12$
Divide both sides by 2:
$x = 6$

Step9: Solve for 38

In the left - hand side triangle of 38, using the angle - sum property of a triangle ($180^{\circ}$ in a triangle), for the triangle with angles $42^{\circ},y^{\circ},x^{\circ}$:
$x + y+42=180$.
For the parallel - line related angles, we know that the angle corresponding to $25^{\circ}$ and $x$ are related. Since the lines are parallel, the angle corresponding to $25^{\circ}$ and $x$ are congruent, so $x = 25$.
Substitute $x = 25$ into $x + y+42=180$:
$25+y + 42=180$
$y=180-(25 + 42)=113$.
For the other triangle with angles $76^{\circ},y^{\circ},z^{\circ}$, since $y = 113$ is an exterior angle, $y=76 + z$. So $z=y - 76=113 - 76 = 37$.
For the angle $w$, using the vertical - angle property, $w$ is vertical to the angle in the triangle with $x$ and $42^{\circ}$, so $w=180-(42 + 25)=113$.

Step10: Solve for 39

Since the triangle is isosceles (two angles are $65^{\circ}$), $x = 65$.
Using the angle - sum property of a triangle in the smaller triangle with angles $65^{\circ},y^{\circ},w^{\circ}$, and since the lines are parallel, $w = 65$.
$y=180-(65 + 65)=50$.
$z$ is vertical to $y$, so $z = 50$.

Answer:

34.
Angle pair name: Alternate exterior angles
Relationship: congruent
Equation: $14x - 1=12x + 17$
$x = 9$

35.
Angle pair name: Alternate interior angles
Relationship: congruent
Equation: $4x-46 = 5x - 44$
$x=-2$

36.
Angle pair name: Corresponding angles
Relationship: congruent
Equation: $5x-15=x + 25$
$x = 10$

37.
Angle pair name: Vertical angles
Relationship: congruent
Equation: $10x-7=8x + 5$
$x = 6$

38.
$w = 113$
$x = 25$
$y = 113$
$z = 37$

39.
$w = 65$
$x = 65$
$y = 50$
$z = 50$