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E. Answer the following.

1. Two angles are in the ratio 3 : 5. If each angle is increased by 30°, then they become supplementary
angles. Find the magnitude of each angle.
2. Two angles A and B are supplementary. If ∠A = 2x + 5° and ∠B = x – 5°, find the measure of both
angles.
3. The sum of two adjacent angles is 52°. If one of them measures 30° more than the other, find the angles.

4. Find the angle whose complement is equal to two-fifth of its supplement.
5. If the measures of two supplementary angles are consecutive odd integers. Find the angles.
6. In the given figure, AB and CD are parallel lines and EH is a transversal. What is the measure of
∠AFE?
C
H
54°
A G
F D
E
B
7. Iron rods a, b, c, d, e and f are making a design of a bridge as shown in following figure, in which
a || b, c || d, e || f. Find the marked angles between
e
(a) b and c 75°
(b) d and e d b c a

(c) d and f
120°
(d) c and f 30° f x a
b f
8. A star is made with the help of line segments a, b, c, d, e and f, in which a || c e z
d, b || e and c || f. If an angle is marked as 120° as shown in the given figure, d
y
then find the ∠x, ∠y and ∠z.
9. A new town is being developed based on the layout of ancient cities like those from the Indus
Civilization. The town is designed with two main parallel streets, Street A and Street B, running
east to west. Several transversal roads, such as Road X and Road Y, intersect these parallel streets
at various points, forming a grid-like pattern. CASE STUDY
Here are some details:
• Street A and Street B are 200 metres apart.
• Road X intersects Street A at a 90° angle and meets Street B at the same angle.
• Road Y is another transversal, intersecting Street A and Street B at right angles, 150 metres east
of Road X.
Based on this scenario, answer the following questions:
(a) If a person stands at the crossing of Street A and Road X, what is the shortest distance
to Street B if he travels along Road X?
(b) If the town planning authority wants to build a new Road Z parallel to Road X to the
east direction, how far from Road X should Road Z be, so that the distance between the
roads Z and Y is 270 m from the west of road Y?
(c) If the angles formed between Street A and the transversal Road Y are all right angles,
what are the corresponding and alternate interior angles formed at the intersections of
Street B and Road Y? Explain your answer.

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