Question

$\text{In}\Delta ABC,\text{the measure of}\angle ACD\text{is}{105}^{\circ }.$
$\text{If}\angle B={65}^{\circ },\text{then find}\angle A.$

• A. ${35}^{\circ }$
• B. ${30}^{\circ }$
• C. ${40}^{\circ }$
• D. ${50}^{\circ }$

Answer 1

The correct option is C ${40}^{\circ }$


The exterior angle property states that the exterior angle of a triangle is equal to the sum of its opposite interior angles.

$\Rightarrow \angle A+\angle B=\angle ACD$
$\Rightarrow \angle A+{65}^{\circ }={105}^{\circ }$
$\Rightarrow \angle A={105}^{\circ }-{65}^{\circ }$
$\Rightarrow \angle A={40}^{\circ }$