Question

In the following figure, side BA of triangle ABC is extended upto D, and DE || CB. If $\angle ADE={70}^{\circ }$ and $\angle ACB={40}^{\circ }$, find the measure of $\angle BAC.$

• A. ${80}^{\circ }$
• B. ${70}^{\circ }$
• C. ${100}^{\circ }$
• D. ${110}^{\circ }$

Answer 1

The correct option is B ${70}^{\circ }$

Given: DE || CB
$\angle ADE={70}^{\circ }$
$\angle ACB={40}^{\circ }$
Since DE || CB and BD is the transversal, alternate interior angles will be equal.
$\Rightarrow \angle EDB=\angle ABC={70}^{\circ }$

In $△ABC$ ,
$\angle ABC+\angle BAC+\angle ACB={180}^{\circ }$
(Sum of all the interior angles of a triangle is ${180}^{\circ }$)
$\Rightarrow {70}^{\circ }+\angle BAC+{40}^{\circ }={180}^{\circ }$
$\Rightarrow \angle BAC={180}^{\circ }-{70}^{\circ }-{40}^{\circ }={70}^{\circ }$
$\Rightarrow \angle BAC={70}^{\circ }$