Question

Measure and classify each angle.

Answer 1

Step 1. Find the acute angles from the figure :

An acute angle is defined as that angle whose measure is less than $90°$ whereas an angle whose measure is equal to ${90}^{°}$is a right angle.

Refer to figure,

Therefore, it is clear that $\angle AOB\text{\hspace{0.17em}and\hspace{0.17em}}\angle BOC$ are acute angles have measure $40°\text{and}85°$ respectively.

Step 2. Find the obtuse angles and straight from the figure :

An obtuse angle is defined as that angle whose measure is more than $90°$ and a straight angle has a measure of $180°$.

Refer to figure,

Therefore, it is clear that $\angle AOC,\angle DOC\text{\hspace{0.17em}and\hspace{0.17em}}\angle DOA$ are obtuse angles have measure $125°,95°\text{\hspace{0.17em}and\hspace{0.17em}}220°$ respectively and $\angle DOB$is a straight angle.

Step 3. Find the reflexive angle.

A reflexive angle is an angle that is more than ${180}^{°}$ and less than ${360}^{°}$.

Refer to figure,

Therefore, it is clear that $\angle DOA$is a reflexive angle of measure ${220}^{°}$.

Hence, the measure of the angles $\angle AOB,\angle AOC,\angle BOC,\angle DOC,\angle DOA\text{\hspace{0.17em}and\hspace{0.17em}}\angle DOB$ are $40°,125°,85°,95°,220°\text{and}180°$ respectively.