Question

In the given figure, $\angle B={65}^{\circ }$and$\angle C={45}^{\circ }$ in$\Delta ABC$ and $DAE\parallel BC$. If $\angle DAB=x^{\circ }$ and $\angle EAC=y^{\circ }$, find the values of $x$ and $y$.​

Answer 1

Given:

$\angle B={65}^{\circ }$, $\angle C={45}^{\circ }$

$DAE\parallel BC$

We know that, when the lines are parallel, then their corresponding angles are equal and their alternate interior angles are equal

$\Rightarrow x=\angle B={65}^{\circ }$ [Since, alternate angles when $AB$ is taken as the transversal]

$\Rightarrow y=\angle C={45}^{\circ }$ [Since, alternate angles when $AC$ is taken as the transversal]

$\therefore x=={65}^{\circ },y={45}^{\circ }$