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In Fig. 6.7, PQ = PS. The value of x is
a. 35°
b. 45°
c. 55°
d. 70°

Solution:

Given, PQR is a triangle.

Also, PQ = PS

We have to find the value of x.

The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles of the triangle.

Considering triangle PQS,

By exterior angle property,

∠PSQ + ∠QPS = 110°

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.

So, ∠PSQ + ∠QPS + ∠PQS = 180°

∠PQS = 180° - 110°

∠PQS = 70°

Considering triangle PRS,

By exterior angle property,

∠PSQ = x + 25°

x = 70° - 25°

x = 45°

Therefore, the value of x is 45°.

✦ Try This: Can a triangle have all angles greater than 60 degrees. Justify your answer

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6

NCERT Exemplar Class 7 Maths Chapter 6 Problem 3

In Fig. 6.7, PQ = PS. The value of x is: a. 35°, b. 45°, c. 55°, d. 70°

Summary:

In Fig. 6.7, PQ = PS. The value of x is 45°

☛ Related Questions:

In Fig. 6.7, PQ = PS. The value of x is a. 35° b. 45° c. 55° d. 70°

In Fig. 6.7, PQ = PS. The value of x is: a. 35°, b. 45°, c. 55°, d. 70°

In Fig. 6.7, PQ = PS. The value of x is
a. 35°
b. 45°
c. 55°
d. 70°