Q. 34.0( 12 Votes )

# In Fig. 6.7, PQ = PS. The value of x is

A. 35°

B. 45°

C. 55°

D. 70°

Answer :

Given: In ΔPQS

PQ = PS, Exterior angle with Q is 110°

In ΔPSR

∠PRS = 25°, ∠RPS = x

**Formula Used/Theory:-**

Exterior angle of triangle is equal to sum of 2 opposite interior angles .

As RQ is straight line

∠PQS + 110° = 180°

∠PQS = 180° - 110°

∠PQS = 70°

As ΔPQS is isosceles triangle and PQ = PS

∴ ∠PQS = ∠PSQ

⇒ ∠PSQ = 70°

In ΔPSR

With exterior angle ∠PSQ equal to sum of opposite interior angles

∠PSQ = ∠SPR + ∠PRS

70° = x + 25°

x = 70° - 25°

x = 45°

Rate this question :

In a right-angled triangle, the angles other than the right angle are

NCERT - Exemplar MathematicsIn Fig. 6.34, find the measures of ∠PON and ∠NPO.

NCERT - Exemplar Mathematics

Find the values of x and y in Fig. 6.37. Plan a Strategy

NCERT - Exemplar Mathematics

In Δ ABC, if ∠A = ∠C, and exterior angle ABX = 140°, then find the angles of the triangle.

NCERT - Exemplar MathematicsIn triangle XYZ, the measure of angle X is 30° greater than the measure of angle Y and angle Z is a right angle. Find the measure of ∠Y.

NCERT - Exemplar MathematicsIn a triangle ABC, the measure of angle A is 40° less than the measure of angle B and 50° less than that of angle C. Find the measure of ∠A.

NCERT - Exemplar MathematicsIn Fig. 6.31(i) and (ii), find the values of a, b and c.

NCERT - Exemplar Mathematics

In Fig. 6.30, find the value of x.

NCERT - Exemplar Mathematics

The measure of three angles of a triangle are in the ratio 5 : 3 : 1. Find the measures of these angles.

NCERT - Exemplar Mathematics