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°.
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