Question

For the given polygon, find the angle ∠CDE.

degrees

Answer 1

In the figure, $\angle D^{/}DC$ is an exterior angle of the corresponding interior angle $\angle CDE.$
The exterior angle $\angle D^{/}DC$ is formed by extending the side DE.

We know that the sum total of a pair of exterior angle and corresponding interior angle is ${180}^o.$
$\Rightarrow \angle D^{/}DC+\angle CDE={180}^o$
$\Rightarrow {75}^o+\angle CDE={180}^o$
$\Rightarrow \angle CDE={180}^o-{75}^o={105}^o$