Question

Find the value of x, y and z in the figure given below. [3 Marks]

Answer 1

$\angle BGH=\angle AGE={110}^{\circ }$ (Since vertically opposite angles are equal)
$\Rightarrow x={110}^{\circ }$ [1 Mark]

$\angle CHG=\angle BGH={110}^{\circ }$ (Since alternate interior angles are equal)
$\Rightarrow y={110}^{\circ }$ [1 Mark]

$\angle BGH+\angle GHD={180}^{\circ }$ (Since co-interior angles are supplementary)
$\Rightarrow z={180}^{\circ }-{110}^{\circ }$
$\Rightarrow z={70}^{\circ }$ [1 Mark]

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