The vertical angle A of an isosceles triangle ABC is two times th
| The vertical angle A of an isosceles triangle ABC is two times the angle B of it. The measure of the angle A is
A. 90°
B. 108°
C. 100°
D. 36°
Please scroll down to see the correct answer and solution guide.
Right Answer is: A
SOLUTION
Given, triangle ABC is isosceles, and angle A is vertical angle,
∴ ∠B = ∠C
Given, vertical angle A of an isosceles triangle ABC is two times the angle B of it
⇒ ∠A = 2∠B
Sum of interior angles of the triangle is 180°.
∠A + ∠B + ∠C = 180°
⇒ 4 ∠B = 180°
⇒ ∠B = 45°
∴ ∠A = 90°