Question

Question 22

Fill in the blanks to make the statements true.

In the given figure,

a) $\angle AOD$ is a/an______angle.

b) $\angle COA$ is a/an______angle.

c) $\angle AOE$ is a/an______angle.

Answer 1

a) Right
Since, $\angle AOD=\angle AOB+\angle BOC+\angle COD$
= ${30}^{\circ }+{20}^{\circ }+{40}^{\circ }={90}^{\circ }$
So, $\angle AOD={90}^{\circ }$ is a right angle.

b) Acute
Since, $\angle COA=\angle COB+\angle BOA$
= ${20}^{\circ }+{30}^{\circ }={50}^{\circ }$
Because $\angle COA={50}^{\circ }<{90}^{\circ }$

So, $\angle$ COA is an acute angle.

c) Obtuse
Since, $\angle AOE=\angle AOB+\angle BOC+\angle COD+\angle DOE$
= ${30}^{\circ }+{20}^{\circ }+{40}^{\circ }+{40}^{\circ }={130}^{\circ }$
Because $\angle AOE={130}^{\circ }>{90}^{\circ }$

So, $\angle$ AOE is an obtuse angle.