Question

Find the values of $x$ and $y$ in figure.

Answer 1

$\angle BAD=\frac{1}{2}\text{exterior}\angle BOD$

$\left[\text{angle subtended by major arc}BD\text{at the center is double the angle subtended by this arc at any other point on the circumferenece}\right]$

$⟹\angle BAD=\frac{1}{2}\times {210}^{\circ }$ $[\because \text{exterior}\angle BOD={360}^{\circ }-{150}^{\circ }={210}^{\circ }]$

$⟹x={105}^{\circ }$

$\angle BCD=\frac{1}{2}\angle BOD=\frac{1}{2}\times {150}^{\circ }$

$\left[\text{angle subtended by minor arc}BD\text{at the center is double the angle subtended by this arc at any other point on the circumferenece}\right]$

$⟹y={75}^{\circ }$