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5. If two complementary angles are in the ratio 1 : 3, find the measure of angles.

6. One of two supplementary angles is 24° more than the measure of the smaller one. Find their
measures.

7. An angle is two-third of its complement. What is the degree measure of the angle?
8. One-third of the supplement of an angle is equal to 10° more than its complement. Find the angle.
9. Find the value of x in the following figures:
(a) (b)
D C
7x + 22°
8x 3x – 4°
x + 3° x – 1° A O B

x + 1°

10. In the given figure, ∠XYZ = 64° and XY is produced to a point P. If ray YQ bisects ∠ZYP, find ∠XYQ
and reflex ∠QYP.

Z Q

64°
X Y P

Knowledge Desk

Our country is situated to the north of the equator between 8°4' (eight degree four minutes) north to
37°6' (Thirty-seven degree six minutes) north latitude and 68°7' (Sixty-eight degree seven minutes) east
to 97°25' (Ninety-seven degree twenty-five minutes) east longitude.
1
(Q 1 degree = 60 minutes & 1 minute = degree)
60
Pair of Lines

Intersecting Lines

l 1
When two lines in a plane intersect at a point, then these lines are called
intersecting lines and the point at which they intersect is called the point of O
intersection. In the figure, l and l are two intersecting lines and O is the point l 2
1
2
of intersection of lines l and l .
1
2
There are some examples of intersecting lines in day-to-day life.
Quick Check
Find some examples from
your surroundings where lines
intersect at right angles and
make a list here.

Sometimes when two lines intersect, they meet at 90° angle. Remember
These intersecting lines are called perpendicular lines. Two straight lines in a plane
intersect exactly at one point.

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