In Fig. 5.11, if AB || CD, ∠ APQ = 50° and ∠PRD = 130°, then ∠ QPR is
a. 130°
b. 50°
c. 80°
d. 30°

Solution:

Given, AB || CD

∠APQ = 50° and ∠PRD = 130°

We have to find the measure of ∠QPR.

Considering the parallel lines AB and CD cut by a transversal PR,

We know that the sum of alternate interior angles on the same side of the transversal is 180 degrees.

So, ∠BPR + ∠PRD = 180°

∠BPR + 130° = 180°

∠BPR = 180° - 130°

∠BPR = 50°

We know that the sum of angles on a straight line is always equal to 180 degrees.

So, ∠APQ + ∠QPR + ∠PRD = 180°

50° + ∠QPR + 50° = 180°

100° + ∠QPR = 180°

∠QPR = 180° - 100°

Therefore, ∠QPR = 80°

✦ Try This: In the given figure, AOB is a straight line, ∠AOC = 68° and ∠BOC = x°. Find x.

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

NCERT Exemplar Class 7 Maths Chapter 5 Problem 10

In Fig. 5.11, if AB || CD, ∠ APQ = 50° and ∠PRD = 130°, then ∠ QPR is: a. 130°, b. 50°, c. 80°, d. 30°

Summary:

In Fig. 5.11, if AB || CD, ∠ APQ = 50° and ∠PRD = 130°, then ∠ QPR is 80°.

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