Question

What is the value $x$ and $y$?

• A. ${15}^{\circ },{15}^{\circ }$
• B. ${15}^{\circ },{18}^{\circ }$
• C. ${18}^{\circ },{15}^{\circ }$
• D. ${18}^{\circ },{18}^{\circ }$

Answer 1

The correct option is B ${15}^{\circ },{18}^{\circ }$

$\text{AB}$ is diameter of the circle.
In $△\text{ADB}$,
$m\angle \text{BDA}={90}^{\circ }$
(angle subtended by diameter $\text{AB}$ on point $\text{D}$ will be ${90}^{\circ }$)
$\Rightarrow x^{\circ }+5x^{\circ }+{90}^{\circ }={180}^{\circ }$
$6x^{\circ }={90}^{\circ }$
$\therefore x={15}^{\circ }$

Now,
In $△\text{ACB}$,
$m\angle \text{ACB}={90}^{\circ }$
(angle subtended by diameter $\text{AB}$ on point $\text{C}$ will be ${90}^{\circ }$)
$\Rightarrow 3y^{\circ }+2y^{\circ }+{90}^{\circ }={180}^{\circ }$
$5y^{\circ }={90}^{\circ }$
$\therefore y={18}^{\circ }$