In the given figure, find the angle measure x.

Question:

In the given figure, find the angle measureĀ x.

Solution:

Sum of all the interior angles of an $\mathrm{n}$-sided polygon $=(n-2) \times 180^{\circ}$

$m \angle A D C=180-50=130^{\circ}$

$m \angle D A B=180-115=65^{\circ}$

$m \angle B C D=180-90=90^{\circ}$

$m \angle A D C+m \angle D A B+m \angle B C D+m \angle A B C=(n-2) \times 180^{\circ}=(4-2) \times 180^{\circ}=2 \times 180^{\circ}=360^{\circ}$

$\Rightarrow m \angle A D C+m \angle D A B+m \angle B C D+m \angle A B C=360^{\circ}$

$\Rightarrow 130^{\circ}+65^{\circ}+90^{\circ}+m \angle A B C=360^{\circ}$

$\Rightarrow 285^{\circ}+m \angle A B C=360^{\circ}$

$\Rightarrow m \angle A B C=75^{\circ}$

$\Rightarrow m \angle C B F=180-75=105^{\circ}$

$\therefore \mathrm{x}=105$

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Fakeha khan
May 31, 2023, 6:35 a.m.
Hi Hello