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 \(\angle BAC.\)

Answer 1

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