Question

In the given figure, what is the measure of q?

• A. ${48}^{\circ }$
• B. ${90}^{\circ }$
• C. ${42}^{\circ }$
• D. ${110}^{\circ }$

Answer 1

The correct option is A ${48}^{\circ }$

Clearly $p={360}^{\circ }-{270}^{\circ }={90}^{\circ }\left(\text{Angles at a point}\right)$

Through C, draw a line l parallel to AB and DE.

$\therefore {42}^{\circ }+x={180}^{\circ }$ and $q+y={180}^{\circ }$
$\Rightarrow x={180}^{\circ }-{42}^{\circ }={138}^{\circ }$
$\therefore y={270}^{\circ }-{138}^{\circ }={132}^{\circ }$
$\therefore q={180}^{\circ }-{132}^{\circ }={48}^{\circ }$