Question

In the adjoining figure, if line m II line n and line p is a transversal then find x.

• A. ${90}^o$
• B. ${50}^o$
• C. ${45}^o$
• D. ${135}^o$

Answer 1

The correct option is C ${45}^o$

Let us mark the points P and Q on m; R and S on n; A and B on p.

Suppose PQ and AB interesect at M, RS and AB intersect at N.

Since, m||n and p is a transversal, then
$m\angle QMN+m\angle SNM={180}^o$
[Interior angles on the same side of transversal are supplementary]

Substituing the values in the above equation, we get
$3x+x={180}^o$
$\Rightarrow 4x={180}^o$
$\Rightarrow x=\frac{{180}^o}{4}$
$\therefore x={45}^o$