Question

In the given figure, QP II ML and other angles are shown. Find the value of x

• A. ${60}^o$
• B. ${35}^o$
• C. ${20}^o$
• D. ${30}^o$

Answer 1

The correct option is D ${30}^o$

Construction : EXTENT the point A to point G and extent point G to a point H such that $PQ||AG||HB||ML$

PROOF : $QPA=PAG={15}^{\circ }$ {Alternate interior angle as $QP||AG$ and AP transversal}

$PAB=PAG+BAG$

$15+BAG={35}^{\circ }-BAG={20}^{\circ }$

$BAG=ABH={20}^{\circ }$(A.I.A as $AG//BH$ and $AB$ transversal)

$LMB=MBH={10}^{\circ }-\left(2\right)$ (A.I.A as $BH//ML$ and $MB$ tranversal)

$MBA=MBH+ABH=x$

From (1),(2) and (3), We Get

$x={20}^{\circ }+{10}^{\circ }$ $\therefore x={30}^{\circ }$