Classification of Angles
by

Inna Buff, Sabrina Lowrie, and Lisa Mann

An angle is the union of two rays having the same endpoint. The endpoint is called the vertex of the angle. The rays are called the sides of the angle. The size of an angle is measured in degrees, denoted by this symbol: x°

Objects of the same shape and size are said to be congruent. Angles are congruent if they have the same degree measure.

An L-shaped angle is called a right angle. A right angle will always measure 90°. Therefore, all right angles are congruent. Lines that intersect to form right angles are said to be perpendicular. In other words, perpendicular lines form right angles.

An angle whose sides form a straight line is called a straight angle and has a measure of 180°.

An acute angle is an angle whose measure is between 0° and 90°.

An obtuse angle is an angle whose measure is between 90° and 180°.

Many special relationships exist between pairs of angles.

Let's take a look at them . . .

Two angles are adjacent if they have the same vertex and share a common side, but do not overlap or have any points in common.

Two angles are complementary if the sum of their measures is 90°. When this occurs, either angle is called the complement of the other. Complementary angles are not necessarily adjacent.

When two angles are adjacent and complementary, do you know what type of angle is formed by their exterior sides??

Two angles are supplementary if the sum of their measures is 180°. When this occurs, either angle is called the supplement of the other. Supplementary angles are not necessarily adjacent.

When two angles are adjacent and supplementary, do you know what type of angle is formed by their exterior sides??

When two lines intersect, they always form four angles with a common vertex. Each pair of angles which are not adjacent (and therefore opposite) are called vertical angles and are equal in measure.

Let's try some Practice Problems !

1. If two angles are supplementary, find the measure of the smaller angle if the measures of the two angles are in the ratio of: a) 1 : 8 b) 3 : 5
2. If two angles are complementary, find the measure of the smaller angle if the measures of the two angles are in the ratio of: a) 2 : 3 b) 3 : 1
3. The measure of the supplement of an angle is three times as great as the measure of the complement of the same angle. What is the measure of the angle?
4. The difference between the measures of an angle and its complement is 14. Find the measure of the smaller of the two angles.
5. The difference between the measures of an angle and its supplement is 22. Find the measure of the smaller of the two angles.