Question

In a $∆\mathrm{ABC}$, $\angle A+\angle B=144°$ and $\angle A+\angle C=124°$ then $\angle B=$

• A. $56°$
• B. $60°$
• C. $65°$
• D. $45°$

Answer 1

The correct option is A

$56°$

Given, $\angle A+\angle B=144°.....\left(1\right)$
$\angle A+\angle C=124°.....\left(2\right)$

In $△\mathrm{ABC}$,
$\angle A+\angle B+\angle C=180°.....\left(3\right)$ [By angle sum property]

Adding equation $\left(1\right)$ and $\left(2\right)$
$\Rightarrow \angle A+\angle B+\angle A+\angle C=144°+124°.....\left(4\right)$.

On putting the equation $\left(3\right)$ in the equation $\left(4\right)$
$\Rightarrow \angle A+180°=268°$
$\Rightarrow \angle A=88°$

Substitute $\angle A=88°$ in equation $\left(1\right)$
$\Rightarrow 88°+\angle B=144°$

$\angle B=56°$

Hence, option $\left(\mathrm{A}\right)$ is the correct answer.