In Fig. 6.12, PQ = PR, RS = RQ and ST || QR. If the exterior angle RPU is 140°, then the measure of angle TSR is
a. 55°
b. 40°
c. 50°
d. 45°
Solution:
Given, PQ = PR, RS = RQ and ST || QR.
The exterior angle RPU is 140°
We have to find the measure of the angle TSR.
Linear pairs of angles are formed when two lines intersect each other at a single point.
Linear pair angles are supplementary angles as their sum is 180°.
∠1 + ∠P = 180°
∠1 + 140° = 180°
∠1 = 180° - 140°
∠1 = 40°
We know that the angles opposite to the equal sides are equal.
Since PQ = PR, ∠Q = ∠R ------------------------------ (1)
By angle sum property of a triangle,
We know that the sum of all the three interior angles of the triangle is equal to 180 degrees.
Considering triangle PQR,
∠P + ∠Q + ∠R = 180°
From (1),
40° + ∠R + ∠R = 180°
2∠R = 180° - 40°
∠R = 140°/2
∠R = 70°
So, ∠Q = ∠R = 70°
Since RS = RQ, ∠Q = ∠S ----------------------------- (2)
Considering triangle SQR,
∠S + ∠Q + ∠R = 180°
From (2),
∠S + ∠S + ∠R = 180°
2∠S + ∠R = 180°
2(70°) + ∠R = 180°
140° + ∠R = 180°
∠R = 180° - 140°
∠R = 40°
Given, ST || QR
If two parallel lines are intersected by a transversal, each pair of alternate interior angles is equal.
So, ∠TSR = ∠SRQ
From the figure,
∠SRQ = 40°
Therefore, ∠TSR = 40°
✦ Try This: In △ ABC, ∠A = 100°, AD bisects ∠A and AD ⊥ BC. Find ∠ B
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 23
In Fig. 6.12, PQ = PR, RS = RQ and ST || QR. If the exterior angle RPU is 140°, then the measure of angle TSR is: a. 55°, b. 40°, c. 50°, d. 45°
Summary:
In Fig. 6.12, PQ = PR, RS = RQ and ST || QR. If the exterior angle RPU is 140°, then the measure of angle TSR is 40°
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