Question

Find angles x and y.

• A. $x={47}^{\circ },y={25}^{\circ }$
• B. $x={27}^{\circ },y={45}^{\circ }$
• C. $x={45}^{\circ },y={27}^{\circ }$
• D. $x={25}^{\circ },y={47}^{\circ }$

Answer 1

The correct option is C

$x={45}^{\circ },y={27}^{\circ }$

Given BE || CD, $\angle$AEB = $\angle$EDC {They are corresponding angles}
$x^{\circ }={45}^{\circ }$
In $\Delta ACD,x^{\circ }+y^{\circ }+{108}^{\circ }={180}^{\circ }$
{Angle sum property}
$\Rightarrow {45}^{\circ }+y+{108}^{\circ }={180}^{\circ }\Rightarrow y={180}^{\circ }-{153}^{\circ }={27}^{\circ }\therefore x={45}^{\circ },y={27}^{\circ }$