Question

The values of $x$ and $y$ in the below figure are ___ and ___ respectively.

• A. ${25}^{\circ }$ and ${60}^{\circ }$
• B. ${40}^{\circ }$ and ${60}^{\circ }$
• C. ${60}^{\circ }$ and ${25}^{\circ }$
• D. ${40}^{\circ }$ and ${25}^{\circ }$

Answer 1

The correct option is D ${40}^{\circ }$ and ${25}^{\circ }$

Consider the cyclic quadrilateral ABCD. Since opposite angles are supplementary,
$\angle A+\angle C={180}^{\circ }\Rightarrow 2x+4+4y-4=180$
$\Rightarrow x+2y={90}^{\circ }....\left(i\right)$
Similarly,
$\angle B+\angle D={180}^{\circ }\Rightarrow x+10+5y+5={180}^{\circ }$
$\Rightarrow x+5y={165}^{\circ }....\left(ii\right)$
On substracting (i) from (ii), we get
$3y=75\Rightarrow y={25}^{\circ }.$
(i) $⟹x={90}^{\circ }-2y={90}^{\circ }-{50}^{\circ }={40}^{\circ }$