Question

In the figure, x, y and z are the internal angles of ∆ABD. Line ED || AB and side AD is extrapolated to point P and the value of $\angle$EDP and $\angle$EDB are n and m, respectively. If $x$ and $z$ are ${75}^{\circ }$ and ${55}^{\circ }$ respectively, find the value of $m+n$.

• A. ${125}^{\circ }$
• B. ${135}^{\circ }$
• C. ${85}^{\circ }$
• D. ${95}^{\circ }$

Answer 1

The correct option is A

${125}^{\circ }$

Since x, y and z are the angles of a triangle, $x+y+z=180$
Given that $x={75}^{\circ }$ and $z={55}^{\circ }$

So, $y={180}^{\circ }-{75}^{\circ }-{55}^{\circ }={50}^{\circ }$
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)

m = x

and

$\angle$BAD = $\angle$EDP (corresponding angles)

i.e. n = y
$m+n=x+y={125}^{\circ }$