Question

In the figure, given below, ABCD is a trapezium. EF is parallel to AD and BC. Find the measure of the angles marked x, y and z.

• A. $x=z={60}^{\circ }$ and $y={60}^{\circ }$
  
• B. $x=z={50}^{\circ }$ and $y={50}^{\circ }$
• C. $x=z={50}^{\circ }$ and $y=6^{\circ }$
• D. $x=z={50}^{\circ }$ and $y={60}^{\circ }$

Answer 1

The correct option is D $x=z={50}^{\circ }$ and $y={60}^{\circ }$

Given, $AD\parallel EF\parallel BC$,
hence, $\angle z=\angle DAC=\angle ACB$ (Alternate angles)
Thus, $x=z={50}^{\circ }$
Now, $\angle ADF+\angle EFD=180$ (Angles between parallel lines)
$y+120=180$
$y={60}^{\circ }$