Question

In the figure below, lines XY and MN intersect at point O. If OP is perpendicular to XY and A = 30${}^{\circ }$, find C.

• A. ${50}^{\circ }$
• B. ${120}^{\circ }$
• C. ${130}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is B ${120}^{\circ }$

Given that,

A = 30${}^{\circ }$

OP is perpendicular to XY

$⟹\angle XOP={90}^{\circ }$

$⟹A+B={90}^{\circ }$

$⟹{30}^{\circ }+B={90}^{\circ }$

$⟹B={90}^{\circ }-{30}^{\circ }$

$⟹B={60}^{\circ }$

Also, MON is a line, so that,

$B+C={180}^{\circ }$

${60}^{\circ }+C={180}^{\circ }$

$C={180}^{\circ }–{60}^{\circ }={120}^{\circ }$