english medium year :2025-26
assignment-4 (semester - i)
class: vii sub. : math
date :10-09-25 date of submission :16-09-25
l-5

l-5

❖ fill in the blanks.
1) a line segment has ______ end point.
2) the supplementary angle of 45° is ______.
3) ______ angle is formed when one arm is common and remaining two arms are on either side.
4) if a line is a transversal to three lines then ____ points of intersections will be formed.
5) the complementary angle of 54° is ______.
6) the measure of right angle is ______.
❖ do as directed.
1) name the pair of angles in each figure.
(a) figure (b) figure
(c) figure (d) figure
2) find the angle which is equal to its supplement.
❖ in the adjoining figure, identify the following.
1) the pair of alternate interior angles.
2) the pair of corresponding angles.
3) the vertically opposite angles.
figure

❖ find the value of x in the following figure if l || m.
1) figure 2) figure
3) figure 4) figure

❖ an angle is greater than 90°. is its supplementary angle greater than 90° or equal to 90° or less than 90°? justify.

Question

english medium year :2025-26
assignment-4 (semester - i)
class: vii sub. : math
date :10-09-25 date of submission :16-09-25
l-5

l-5

❖ fill in the blanks.
1) a line segment has ______ end point.
2) the supplementary angle of 45° is ______.
3) ______ angle is formed when one arm is common and remaining two arms are on either side.
4) if a line is a transversal to three lines then ____ points of intersections will be formed.
5) the complementary angle of 54° is ______.
6) the measure of right angle is ______.
❖ do as directed.
1) name the pair of angles in each figure.
(a) figure (b) figure
(c) figure (d) figure
2) find the angle which is equal to its supplement.
❖ in the adjoining figure, identify the following.
1) the pair of alternate interior angles.
2) the pair of corresponding angles.
3) the vertically opposite angles.
figure

❖ find the value of x in the following figure if l || m.
1) figure 2) figure
3) figure 4) figure

❖ an angle is greater than 90°. is its supplementary angle greater than 90° or equal to 90° or less than 90°? justify.

Accepted Answer

### Fill in the blanks 1. **Step 1: Recall the definition of a line segment** A line segment is a part of a line with two distinct endpoints. Answer: two 2. **Step 1: Recall the definition of supplementary angles** Supplementary angles add up to $ 180^\circ $. Let the supplementary angle of $ 45^\circ $ be $ x $. Then $ 45^\circ + x = 180^\circ $. **Step 2: Solve for $ x $** $ x = 180^\circ - 45^\circ = 135^\circ $ Answer: $ 135^\circ $ 3. **Step 1: Recall the definition of a linear pair (or adjacent supplementary angles)** When two angles share a common arm and their other arms are on opposite sides of the common arm, they form a **linear pair** (or adjacent supplementary angles, summing to $ 180^\circ $). Answer: linear (or supplementary, but "linear pair" is more precise) 4. **Step 1: Analyze intersections of a transversal with three lines** A transversal intersects each of the three lines at one point. So for three lines, the number of intersection points is $ 3 $. Answer: three 5. **Step 1: Recall the definition of complementary angles** Complementary angles add up to $ 90^\circ $. Let the complementary angle of $ 54^\circ $ be $ x $. Then $ 54^\circ + x = 90^\circ $. **Step 2: Solve for $ x $** $ x = 90^\circ - 54^\circ = 36^\circ $ Answer: $ 36^\circ $ 6. **Step 1: Recall the measure of a right angle** A right angle is defined as $ 90^\circ $. Answer: $ 90^\circ $ ### Do as directed (1: Naming angle pairs) *(Note: Since figures are not fully detailed, we use standard angle - pair definitions:)* - **(a)** If the two angles are on the same side of the transversal and between the two lines, they could be **consecutive interior angles** (or if they are on opposite sides, alternate interior, etc.—depends on the figure). Assuming the lines are parallel, if $ \angle1 $ and $ \angle2 $ are on the same side, they might be consecutive interior angles. - **(b)** $ \angle3 $ and $ \angle4 $ share a common vertex and a common side, with their other sides opposite—they are **vertically opposite angles** (or adjacent angles forming a linear pair? Depends on the figure. If the lines are intersecting, vertical angles; if a transversal, maybe corresponding or alternate). - **(c)** $ \angle5 $ and $ \angle6 $: If the lines are parallel and cut by a transversal, they are **corresponding angles** (or alternate interior, depending on position). - **(d)** $ \angle7 $ and $ \angle8 $ form a **linear pair** (they are adjacent and supplementary, summing to $ 180^\circ $). ### Do as directed (2: Angle equal to its supplement) **Step 1: Let the angle be $ x $** Its supplement is also $ x $ (given). Supplementary angles sum to $ 180^\circ $, so $ x + x = 180^\circ $. **Step 2: Solve for $ x $** $ 2x = 180^\circ \implies x = \frac{180^\circ}{2}=90^\circ $ Answer: $ 90^\circ $ ### In the adjoining figure (angle identification) *(Assuming lines $ a \parallel b $ cut by a transversal:)* 1. **Alternate interior angles**: Angles between the two parallel lines and on opposite sides of the transversal. E.g., $ \angle4 $ and $ \angle5 $, $ \angle3 $ and $ \angle6 $. 2. **Corresponding angles**: Angles in the same relative position at each intersection. E.g., $ \angle1 $ and $ \angle5 $, $ \angle2 $ and $ \angle6 $, $ \angle3 $ and $ \angle7 $, $ \angle4 $ and $ \angle8 $. 3. **Vertically opposite angles**: Angles opposite each other when two lines intersect. E.g., $ \angle1 $ and $ \angle3 $, $ \angle2 $ and $ \angle4 $, $ \angle5 $ and $ \angle7 $, $ \angle6 $ and $ \angle8 $. ### Find the value of $ x $ (when $ l \parallel m $) 1. **Figure 1**: **Step 1: Identify the angle relationship** $ x $ and $ 65^\circ $ are **corresponding angles** (since $ l \parallel m $ and $ t $ is a transversal). Corresponding angles are equal. Thus, $ x = 65^\circ $ 2. **Figure 2**: **Step 1: Identify the angle relationship** The $ 70^\circ $ angle and $ x $ are **corresponding angles** (since $ l \parallel m $ and $ p $ is a transversal). Corresponding angles are equal. Thus, $ x = 70^\circ $ 3. **Figure 3**: **Step 1: Find the adjacent angle to $ 130^\circ $** The angle adjacent to $ 130^\circ $ on line $ l $ is $ 180^\circ - 130^\circ = 50^\circ $ (linear pair). **Step 2: Identify the angle relationship with $ x $** This $ 50^\circ $ angle and $ x $ are **corresponding angles** (since $ l \parallel m $ and $ n $ is a transversal). Thus, $ x = 50^\circ $ 4. **Figure 4**: **Step 1: Analyze the vertical and parallel line relationships** The $ 110^\circ $ angle and the angle adjacent to $ 70^\circ $ (on line $ l $): Since $ a $ and $ b $ are parallel (vertical lines), the angle adjacent to $ 70^\circ $ is $ 110^\circ $ (corresponding angles). Then $ x $ and $ 70^\circ $: Wait, the $ 70^\circ $ and $ x $: Since $ l \parallel m $ and the transversal is vertical, $ x = 70^\circ $? Wait, no—let's re - check. The $ 110^\circ $ angle: the angle adjacent to it on line $ m $ is $ 70^\circ $ (linear pair). Then $ x $ and $ 70^\circ $ are corresponding angles (since $ l \parallel m $ and the transversal is the vertical line). Thus, $ x = 70^\circ $ ### Angle greater than $ 90^\circ $: Supplementary angle? **Step 1: Let the angle be $ \theta $, where $ \theta>90^\circ $** Let its supplementary angle be $ \phi $. By definition, $ \theta+\phi = 180^\circ $. **Step 2: Solve for $ \phi $** $ \phi=180^\circ - \theta $ Since $ \theta > 90^\circ $, subtracting a number greater than $ 90^\circ $ from $ 180^\circ $ gives $ \phi<90^\circ $. Justification: If $ \theta = 100^\circ $ (example), then $ \phi = 180^\circ - 100^\circ = 80^\circ<90^\circ $. So the supplementary angle is less than $ 90^\circ $. ### Final Answers (Key Points) - Fill in the blanks: $ 2, 135^\circ, \text{linear}, 3, 36^\circ, 90^\circ $ - Angle equal to its supplement: $ 90^\circ $ - $ x $ values: $ 65^\circ, 70^\circ, 50^\circ, 70^\circ $ - Supplementary angle of $ \theta>90^\circ $: less than $ 90^\circ $

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