Question

In the adjacent figure, the pentagon is such that $AB=BC=CD$ and $AE=ED$. Moreover, $\angle ABC=\angle BCD=\angle AED={130}^o$. Find the measure of $\angle BAE$ and $\angle EDC$.

Answer 1

Given a pentagon, $AB=BC=CD$

$\Rightarrow AE=ED$

$\Rightarrow \angle ABC=\angle BCD=\angle AED=130°$

Let $\angle BAE=\angle EDC=x$

The total sum of interior angles of a polygon $=540°$

$\Rightarrow 130°+{130}^o+x+{130}^o+x={540}^o$

$\therefore x=75°$

Hence, the answer is $75°.$