Question

In the given figure, $\angle DBC={22}^{\circ }and\angle DCB={78}^{\circ }$ then $\angle BAC$ is equal to:

• A. ${90}^{\circ }$
• B. ${80}^{\circ }$
• C. ${78}^{\circ }$
• D. ${22}^{\circ }$

Answer 1

The correct option is B ${80}^{\circ }$

Let $\angle BAC=x$

$\therefore \angle BDC=x$ (angle subtended by chord on same segment are equal)

In $\Delta BDC$,

$x+{22}^{\circ }+{78}^{\circ }={180}^{\circ }$

$x+100={180}^{\circ }$

$x={80}^{\circ }=\angle BAC$

Ans (B)