Question

In the pentagon $ABCDE$ shown above, the measures of angles $A,E$ and $C$ are given. It is known that the measures of angles $B$ and $D$ are equal.Then which of the following is true?

• A. $\overline{AB}\parallel \overline{CD}$
• B. $\overline{BC}\parallel \overline{AE}$
• C. $\overline{AB}\parallel \overline{DE}$
• D. $\overline{CD}\parallel \overline{AE}$

Answer 1

The correct option is A $\overline{AB}\parallel \overline{CD}$

In given pentagon $ABCDE$, angle $B$ and $D$ are equal.

Then $120+b+40+b+100=280$

$\Rightarrow 2b=280$

$\Rightarrow b=140$

Then $AB||CD$