Question

In the figure $x,y$ and $z$ are the internal angles of $△ABD.$ Line $ED\parallel AB$ and side $AD$ is extended to point $P$ and the value of $\angle EDP$ and $\angle EDB$ are $n$ and $m,$ respectively. Then, the values of $n$ and $m$ are ______ and _______, respectively.

• A. z, y
• B. x, z
• C. y, z
• D. y, x

Answer 1

The correct option is D

y, x

In the diagram, it is given that the line $ED$ is parallel to side $AB$ of the triangle.

Therefore,

$\angle ABD=\angle BDE$ [alternate interior angles]

$\Rightarrow m=x$

and

$\angle BAD=\angle EDP$ [corresponding angles]

$\Rightarrow n=y$