# In Fig. 5.36, PQ || RS, TR || QU and ∠PTR = 42°. Find ∠QUR

**Solution:**

Given, PQ || RS and TR || QU.

Also, ∠PTR = 42°

We have to find the measure of ∠QUR.

Considering two parallel lines PQ and RS cut by a transversal RT,

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

∠PTR = ∠TRU

So, ∠TRU = 42°

If two parallel lines are intersected by a __transversal__, each pair of interior angles on the same side of the transversal is __supplementary__.

By the above property,

∠TRU + ∠QUR = 180°

42° + ∠QUR = 180°

∠QUR = 180° - 42°

Therefore, ∠QUR = 138°

**✦ Try This:** In the adjoining figure, we have ∠1 =∠3 and ∠2 = ∠4. Show that ∠A = ∠C.

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

**NCERT Exemplar Class 7 Maths Chapter 5 Problem 75**

## In Fig. 5.36, PQ || RS, TR || QU and ∠PTR = 42°. Find ∠QUR

**Summary:**

In Fig. 5.36, PQ || RS, TR || QU and ∠PTR = 42°. The measure of ∠QUR is 138°.

**☛ Related Questions:**

- The drawings below (Fig. 5.37), show angles formed by the goalposts at different positions of a foot . . . .
- The drawings below (Fig. 5.37), show angles formed by the goalposts at different positions of a foot . . . .
- The drawings below (Fig. 5.37), show angles formed by the goalposts at different positions of a foot . . . .

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