Question

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

Answer 1

From the figure

$\angle AOD,\angle DOC,\angle BOC$ are supplementary angles

$⟹\angle AOD+\angle DOC+\angle BOC={180}^{\circ }$

$⟹(x-10{)}^{\circ }+(4x-25{)}^{\circ }+(x+5{)}^{\circ }={180}^{\circ }$

$⟹(6x-30{)}^{\circ }={180}^{\circ }$

$⟹6x-30=180$

$⟹6x=210$

$⟹x=\frac{210}{6}$

$⟹x=35$

$\angle BOC=(x+5{)}^{\circ }=(35+5{)}^{\circ }={40}^{\circ }$