Question

In the given figure, find the value of q.

• A. ${68}^{\circ }$
• B. ${48}^{\circ }$
• C. ${60}^{\circ }$
• D. ${30}^{\circ }$

Answer 1

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

Construction: Through c, draw a line l parallel to AB and DE.

$\therefore 42°+x=180°\text{and}q+y=180°\text{(Co-interior angles)}$

$\Rightarrow x={180}^{\circ }-{42}^{\circ }={138}^{\circ }\text{And,}x+y=270°\Rightarrow 138°+y=270°\therefore y={270}^{\circ }-{138}^{\circ }={132}^{\circ }$

$\text{Then,}q+132°=180°\therefore q={180}^{\circ }-{132}^{\circ }={48}^{\circ }$