Question

In the figure given below, side AE = side CB and AE||CB.
Also, side BA = side ED = side DC and angle A measures 100°.
What is the measure of $\angle DCB$ ?

• A. 150°
• B. 160°
• C. 100°
• D. 120°

Answer 1

The correct option is B 160°

Join the points E and C as shown.Given, side AE and side CB are equal and parallel.
Let us join E and C. Now, ABCE forms a quadrilateral.

Since, in a quadrilateral if a pair of opposite sides are parallel and equal then the quadrilateral is a parallelogram.

Therefore, ABCE form a parallelogram.

We know that opposite angles of a parallelogram are equal.
So, in parallelogram AECB,
$\angle ECB=\angle BAE=100°$

Also,
side EC = side BA = side Ed = side DC
$\therefore △EDC\text{is an equilateral triangle}$
We know that each angle of an euqilateral triangle measures 60°.
$\Rightarrow \angle DCE=60°$

Now,
$\angle DCB=\angle DCE+\angle ECB$
$\Rightarrow \angle DCB=60°+100°=160°$