Question

In a triangle ABC, base angles B and C are equal. If the vertical angle is ${30}^{\circ }$ less than B, then find angle A.

• A. 30°
• B. 40°
• C. 50°
• D. 60°

Answer 1

The correct option is B

40°

Let the base angles 'B' and 'C' be x.

Therefore, the vertical angle= $\angle$A= x-30

We know that the sum of all the angles of a triangle is ${180}^{\circ }$

$\angle$A + $\angle$B + $\angle$C= ${180}^{\circ }$

(x-30) + x + x= ${180}^{\circ }$

3x - 30=${180}^{\circ }$

3x= ${180}^{\circ }$+${30}^{\circ }$= ${210}^{\circ }$

$x=\frac{210}{3}={70}^{\circ }$

Therefore, $\angle$A= x - 30 = 70 - 30 = ${40}^{\circ }$