In Fig 5.58, PQ, RS and UT are parallel lines. If c = 75° and a = 2/5 c, find b.

Solution:

Given, PQ, RS and UT are parallel lines.

c = 75° and a = 2/5 c

We need to find b.

Considering PQ || UT with PT as transversal,

If two parallel lines are intersected by a transversal, each pair of alternate interior angles are equal.

So, ∠QPT = ∠UTP

Now, a + b = c

b = c- a

b = c - 2/5 c

b = 5c - 2c/5

b = 3c/5

b = 3( 75°) /5

b = 45°

Therefore,the value of b is 45°

✦ Try This: In the figure, AB || CD and EF || GH. Find all the pairs of alternate interior angles.

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5

NCERT Exemplar Class 7 Maths Chapter 5 Problem 105 (ii)

In Fig 5.58, PQ, RS and UT are parallel lines. If c = 75° and a = 2/5 c, find b.

Summary:

PQ, RS and UT are parallel lines. If c = 75° and a = 2/5 c,the value of b is 45°

☛ Related Questions:

• In Fig. 5.59, AB||CD. Find the reflex ∠ EFG
• In Fig. 5.60, two parallel lines l and m are cut by two transversals n and p. Find the values of x a . . . .
• In Fig. 5.61, l, m and n are parallel lines, and the lines p and q are also parallel. Find the value . . . .