Question

In the adjoining figure, AOB is a straight line. If x : y : z=4:5 :6, then y =?

(a) ${60}^{\circ }$

(b) ${80}^{\circ }$

(c) ${48}^{\circ }$

(d) ${72}^{\circ }$

Answer 1

ANSWER:
(a) ${60}^{\circ }$
Let
$\angle AOB=x^{\circ }=4a^{\circ },\angle COB=y^{\circ }=5a^{\circ }and\angle BOD=z^{\circ }=6a^{\circ }$
Then, we have:
$\angle AOB+\angle COB+\angle BOD={180}^{\circ }SinceAOBisastraightline\Rightarrow 4a+5a+6a={180}^{\circ }\Rightarrow 15a={180}^{\circ }\Rightarrow a={12}^{\circ }\therefore y=5\times 12°={60}^{\circ }$