Question

Question 100

In the given figure find the value of $\angle BOC$, if points A, O and B collinear.

Answer 1

Since, A, O and B are collinear. Then, AOB will be a straight line and sum of all the angles on a straight line is ${180}^{\circ }$
$\therefore \angle AOD+\angle DOC+\angle COB={180}^{\circ }\Rightarrow (x-10{)}^{\circ }+(4x-25{)}^{\circ }+(x+5{)}^{\circ }={180}^{\circ }\Rightarrow x-{10}^{\circ }+4x-{25}^{\circ }+x+5={180}^{\circ }\Rightarrow 6x-{30}^{\circ }={180}^{\circ }\Rightarrow 6x={180}^{\circ }+{30}^{\circ }\Rightarrow 6x={210}^{\circ }\Rightarrow x={35}^{\circ }Now,\angle BOC=(x+5{)}^{\circ }=(35+5{)}^{\circ }={40}^{\circ }$