Question

Find x, y and z in the figure given below.

• A. $x={70}^{\circ },y={110}^{\circ },z={70}^{\circ }$
• B. $x={110}^{\circ },y={110}^{\circ },z={70}^{\circ }$
• C. $x={110}^{\circ },y={110}^{\circ },z={90}^{\circ }$
• D. $x={110}^{\circ },y={110}^{\circ },z={110}^{\circ }$

Answer 1

The correct option is B

$x={110}^{\circ },y={110}^{\circ },z={70}^{\circ }$

$\angle BGH=\angle AGE={110}^{\circ }$ (Since vertically opposite angles are equal)
$\Rightarrow x={110}^{\circ }$

$\angle CHG=\angle BGH={110}^{\circ }$ (Since alternate interior angles are equal)
$\Rightarrow y={110}^{\circ }$

$\angle BGH+\angle GHD={180}^{\circ }$ (Since co-interior angles are supplementary)
$\Rightarrow z={180}^{\circ }-{110}^{\circ }$
$\Rightarrow z={70}^{\circ }$

$\therefore x={110}^{\circ },y={110}^{\circ }andz={70}^{\circ }$