Question

Given $\angle DCA={20}^o$ and $\angle DEC={115}^o.$ Find the angle $\angle BAC.$

• A. ${30}^o$
• B. ${45}^o$
• C. ${60}^o$
• D. ${80}^o$

Answer 1

The correct option is B ${45}^o$

The given figure is as follows:

From interior angle sum property for $△DCB,$
$\angle BDC+\angle DCA+\angle DEC={180}^o$
$\Rightarrow \angle BDC={180}^o-{20}^o-{115}^o={45}^o$

Consider the arc CB.
The arc subtends angle at point D and at point A on same segment.

We know that the measure of all angles subtended by an arc on the same segment of the circle are equal.

$\therefore \angle BAC=\angle BDC={45}^o$