Question

In the given figure,
$\angle CAE={84}^{\circ }$.
If $\angle B:\angle C=3:4,$ then $\angle B$ = ____ and $\angle C$ = ____.

• A. $\angle B={12}^{\circ },\angle C={72}^{\circ }$
• B. $\angle B={36}^{\circ },\angle C={48}^{\circ }$
• C. $\angle B={75}^{\circ },\angle C={90}^{\circ }$
• D. $\angle B={33}^{\circ },\angle C={44}^{\circ }$

Answer 1

The correct option is B $\angle B={36}^{\circ },\angle C={48}^{\circ }$

Let,
$\angle B=3x^{\circ }$ and $\angle C=4x^{\circ }.$

By Exterior angle property,
$\angle B+\angle C=\angle CAE$
$3x^{\circ }+4x^{\circ }={84}^{\circ }$
$7x={84}^{\circ }$
$\therefore x={12}^{\circ }$

$\therefore \angle B=3\times \left({12}^{\circ }\right)={36}^{\circ }$

$\therefore \angle C=4\times \left({12}^{\circ }\right)={48}^{\circ }$