In ∆ ABC, AB = AC and ∠B = 50°. Then ∠C is equal to
a. 40°
b. 50°
c. 80°
d. 130°

Solution:

From the question,

In ∆ ABC, AB = AC and ∠B = 50°

As AB = AC, ∆ ABC is an isosceles triangle

As the angles opposite to equal sides are equal

∠B = ∠C = 50°

Therefore, ∠C is equal to 50°.

✦ Try This: In ∆ PQR, PQ = PR and ∠Q = 30°. Then ∠R is equal to a. 20°, b. 30°, c. 40°, d. 50°

From the question,

In ∆ PQR, PQ = PR and ∠Q = 30°

As PQ = PR, ∆ PQR is an isosceles triangle

As the angles opposite to equal sides are equal

∠Q = ∠R = 30°

Therefore, ∠R is equal to 30°.

☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 7

NCERT Exemplar Class 9 Maths Exercise 7.1 Problem 3

In ∆ ABC, AB = AC and ∠B = 50°. Then ∠C is equal to, a. 40°, b. 50°, c. 80°, d. 130°

Summary:

Angle sum property states that the sum of interior angles of a triangle is 180°. In ∆ ABC, AB = AC and ∠B = 50°. Then ∠C is equal to 50°

☛ Related Questions:

• In ∆ ABC, BC = AB and ∠B = 80°. Then ∠A is equal to , a. 80°, b. 40°, c. 50°, d. 100°
• In ∆ PQR, ∠R = ∠P and QR = 4 cm and PR = 5 cm. Then the length of PQ is , a. 4 cm, b. 5 cm, c. 2 cm, . . . .
• D is a point on the side BC of a ∆ ABC such that AD bisects ∠BAC. Then , a. BD = CD , b. BA > BD, c. . . . .