Question

In the following figure, $\angle 1=2y+{25}^{\circ },\angle 2=x+{15}^{\circ }$. Find $x$ and $y$, if $2y+{25}^{\circ }=3y$.

• A. $x={60}^{\circ },y={20}^{\circ }$
• B. $x={65}^{\circ },y={25}^{\circ }$
• C. $x={65}^{\circ },y={20}^{\circ }$
• D. $x={60}^{\circ },y={25}^{\circ }$

Answer 1

The correct option is D $x={60}^{\circ },y={25}^{\circ }$

Given: $\angle 1=2y+{25}^{\circ }$
and $\angle 2=x+{15}^{\circ }$
$2y+{25}^{\circ }=3y^{\circ }$

$\Rightarrow {25}^{\circ }=3y-2y=y$
$\Rightarrow y={25}^{\circ }$

$\Rightarrow \angle 1=2y+{25}^{\circ }=2\times 25+25$
$\Rightarrow \angle 1={75}^{\circ }$

Here, both the lines intersect at O, thus vertically opposite angles $\angle 1$ and $\angle 2$ will be equal.
$\Rightarrow \angle 1=\angle 2$
$\Rightarrow \angle 2={75}^{\circ }$
$\Rightarrow x+{15}^{\circ }={75}^{\circ }$
$\Rightarrow x={60}^{\circ }$
Thus, the value of $x={60}^{\circ }$ and $y={25}^{\circ }$.