Question

From the figure given below, find out the measure of $\angle$COB and $\angle$AOC respectively.

• A. 24${}^{\circ }$ and 126${}^{\circ }$
• B. 42${}^{\circ }$ and 156${}^{\circ }$
• C. 24${}^{\circ }$ and 156${}^{\circ }$
• D. 42${}^{\circ }$ and 126${}^{\circ }$

Answer 1

The correct option is C

24${}^{\circ }$ and 156${}^{\circ }$

Since AB is a straight line, $\angle AOB={180}^{\circ }$

Therefore, $\angle AOC+\angle COB={180}^{\circ }$

$\Rightarrow 3x+{30}^{\circ }+2x-{60}^{\circ }={180}^{\circ }$

$\Rightarrow 5x-{30}^{\circ }={180}^{\circ }$

$\Rightarrow 5x={210}^{\circ }$

$\Rightarrow x={42}^{\circ }$

Therefore,

$\angle COB=2x-{60}^{\circ }={84}^{\circ }-{60}^{\circ }={24}^{\circ }$

$\angle AOC=3x+{30}^{\circ }={126}^{\circ }+{30}^{\circ }={156}^{\circ }$