Question

The number of obtuse angles in the given figure is
a) $2$
b) $3$
c) $4$
d) $5$

Answer 1

An obtuse angle is an angle whose measure is more than ${90}^{\circ }$ but less than ${180}^{\circ }$.

There are $4$ obtuse angles which can be formed with the following combination of angles.

(i) $\angle BOC+\angle DOC={30}^{\circ }+{65}^{\circ }={95}^{\circ }$

(ii) $\angle EOD+\angle DOC+\angle COB={45}^{\circ }+{65}^{\circ }+{30}^{\circ }={140}^{\circ }$

(iii) $\angle EOD+\angle DOC={45}^{\circ }+{65}^{\circ }={110}^{\circ }$

(iv) $\angle AOE+\angle EOD+\angle DOC={65}^{\circ }+{45}^{\circ }+{40}^{\circ }$ = ${150}^{\circ }$

Therefore correct option is (c) $4$.