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# In Fig. 5.38, l ||m ||n. ∠QPS = 35° and ∠QRT = 55°. Find ∠PQR

**Solution:**

Given, l ||m ||n

∠QPS = 35° and ∠QRT = 55°

We have to find the measure of ∠PQR.

Considering l || m intersected by __transversal__ PQ,

If two __parallel lines__ are intersected by a transversal, then each pair of alternate interior angles is equal.

∠QPS = ∠PQM

So, ∠PQM = 35°

Considering m || n intersected by transversal RQ,

If two parallel lines are intersected by a transversal, then each pair of __alternate interior angles__ is equal.

∠TRQ = ∠RQM

So, ∠RQM = 55°

From the figure,

∠PQR = ∠PQM + ∠RQM

= 35° + 55°

Therefore, ∠PQR = 90°

**✦ Try This: ** The complementary angle of 65° is

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

**NCERT Exemplar Class 7 Maths Chapter 5 Problem 78**

## In Fig. 5.38, l ||m ||n. ∠QPS = 35° and ∠QRT = 55°. Find ∠PQR

**Summary:**

In Fig. 5.38, l ||m ||n. ∠QPS = 35° and ∠QRT = 55°. The measure of ∠PQR is 90°

**☛ Related Questions:**

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