Question

What is the value of y in the following figure?

• A. ${10}^{\circ }$
• B. ${20}^{\circ }$
• C. ${15}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

The correct option is A ${10}^{\circ }$

$△ABC$ is a right angled triangle. Hence, $\angle BAC$ and $\angle ACB$ are complementary angles.

$\Rightarrow (3y-{30}^{\circ })+(2y+{70}^{\circ })={90}^{\circ }$
$\Rightarrow 5y+{40}^{\circ }={90}^{\circ }$
$\Rightarrow 5y={90}^{\circ }-{40}^{\circ }$
$\Rightarrow 5y={50}^{\circ }$
$\Rightarrow y=\frac{{50}^{\circ }}{5}$
$\Rightarrow y={10}^{\circ }$

Thus, the value of $y$ is ${10}^{\circ }$.