Question:
In the given figure, find the angle measureĀ x.
Solution:
Sum of all the interior angles of an $\mathrm{n}$-sided polygon $=(n-2) \times 180^{\circ}$
$m \angle A D C=180-50=130^{\circ}$
$m \angle D A B=180-115=65^{\circ}$
$m \angle B C D=180-90=90^{\circ}$
$m \angle A D C+m \angle D A B+m \angle B C D+m \angle A B C=(n-2) \times 180^{\circ}=(4-2) \times 180^{\circ}=2 \times 180^{\circ}=360^{\circ}$
$\Rightarrow m \angle A D C+m \angle D A B+m \angle B C D+m \angle A B C=360^{\circ}$
$\Rightarrow 130^{\circ}+65^{\circ}+90^{\circ}+m \angle A B C=360^{\circ}$
$\Rightarrow 285^{\circ}+m \angle A B C=360^{\circ}$
$\Rightarrow m \angle A B C=75^{\circ}$
$\Rightarrow m \angle C B F=180-75=105^{\circ}$
$\therefore \mathrm{x}=105$