Question

A, B, C are the three angles of a triangle. If $\angle B-\angle A={45}^{\circ },\angle B-\angle C={15}^{\circ }$ then, find the values of $\angle A,\angle Band\angle C$ respectively.

• A. 80°, 65°, 35°
• B. 35°, 80°, 65°
• C. 65°, 80°, 35°
• D. None of these

Answer 1

The correct option is B

35°, 80°, 65°

Sum of the angles in a triangle is ${180}^{\circ }$.
$\angle A+\angle B+\angle C={180}^{\circ }\cdots \left(1\right)$
Given that, $\angle B-\angle A={45}^{\circ }$
$\angle A=\angle B-{45}^{\circ }\cdots \left(2\right)$
$\angle B-\angle C={15}^{\circ }$
$\angle C=\angle B-{15}^{\circ }\cdots \left(3\right)$
Putting(2) and (3) in (1)
$\angle B-{45}^{\circ }+\angle B+\angle B-{15}^{\circ }={180}^{\circ }$
$3\angle B-{60}^{\circ }={180}^{\circ }$
$3\angle B={240}^{\circ }$
$\angle B={80}^{\circ }$
$\angle A=\angle B-{45}^{\circ }={80}^{\circ }-{45}^{\circ }={35}^{\circ }$
$\angle C=\angle B-{15}^{\circ }={80}^{\circ }-{15}^{\circ }={65}^{\circ }$