In Fig. 6.3, if OP||RS, ∠OPQ = 110° and ∠QRS = 130°, then ∠PQR is equal to
a) 40°
b) 50°
c) 60°
d) 70°
Solution:
Given, OP||RS
Also, ∠OPQ = 110° and ∠QRS = 130°
We have to find the measure of ∠PQR
Extending OP to meet RQ at X
Given, OP || RS
RX is a transversal
We know that, if a transversal intersects two parallel lines, then the alternate angles are equal.
∠PXR = ∠SRX
Given, ∠QRS = 130°
So, ∠PXR = 130°
From the figure,
RQ is a line segment
PX is a ray initiating from X on the line RQ.
So, the linear pair of angles ∠PXQ + ∠PXR = 180°
∠PXQ + 130° = 180°
∠PXQ = 180° - 130°
∠PXQ = 50°
Considering triangle PQX,
∠OPQ is an exterior angle.
We know that an exterior angle of a triangle is equal to the sum of the corresponding two interior opposite angles.
So, ∠OPQ = ∠PXQ + ∠PQX
Given, ∠OPQ = 110°
110° = 50° + ∠PQX
∠PQX = 110°- 50°
∠PQX = 60°
From the figure,
∠PQX = ∠PQR
Therefore, the measure of ∠PQR is 60°
✦ Try This: Can two obtuse angles be adjacent angles?
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6
NCERT Exemplar Class 9 Maths Exercise 6.1 Problem 7
In Fig. 6.3, if OP||RS, ∠OPQ = 110° and ∠QRS = 130°, then ∠PQR is equal to a) 40°, b) 50°, c) 60°, d) 70°
Summary:
If a transversal intersects two parallel lines, then the alternate angles are equal. In Fig. 6.3, if OP||RS, ∠OPQ = 110° and ∠QRS = 130°, then ∠PQR is equal to 60°
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