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°
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