ANGLES – SIMPLE FIGURES

Concept: Some special angles have specific names. It is important to become familiar with the names and relationships of the most basic of these angles. They include supplementary, complementary, and vertical angles.

Complimentary angles are angles whose sum is . Often, the value of one complementary angle is given, and you are asked to find the value of the other. Simply subtract the value of the given angle from to find the value of the other angle.

Supplementary angles are angles whose sum is . Often, the value of one supplementary angles is given, and you are asked to find the value of the other. Simply subtract the value of the given angle from to find the value of the other angle.

Vertical angles are formed when two straight lines cross at a point. Vertical angles lie across from each other and are equal. The value of the given angle is the same as the value of the other angle.

Steps for Solving Simple Figure Problems

Step 1 | Determine if the figure is a complementary, supplementary, or vertical angle.
Step 2 | If the angle is complementary, subtract the value of the given angle from to find the value of the other angle. Go to Step 5.
Step 3 | If the angle is supplementary, subtract the value of the given angle from . Go to Step 5.
Step 4 | If the angles are vertical, they are equal. The value of the given angle is the same as the value of the other angle. Go to Step 5.
Step 5 | Write the final answer.

Example 1: Given is , what is the measurement of in degrees?

Step 1 | Determine if the figure is a complementary, supplementary, or vertical angle. | complimentary
Step 2 | If the angle is complementary, subtract the value of the given angle from to find the value of the other angle. Go to Step 5. | 90 – 60 = 30
Step 3 | If the angle is supplementary, subtract the value of the given angle from . Go to Step 5. | Does not apply.
Step 4 | If the angles are vertical, they are equal. The value of the given angle is the same as the value of the other angle. Go to Step 5. | Does not apply.
Step 5 | Write the final answer. | =

Example 2: Given angle c = 120 degrees, what is the measure of angle of b in degrees?

Step 1 | Determine if the figure is a complementary, supplementary, or vertical angle. | vertical
Step 2 | If the angle is complementary, subtract the value of the given angle from to find the value of the other angle. Go to Step 5. | Does not apply.
Step 3 | If the angle is supplementary, subtract the value of the given angle from . Go to Step 5. | Does not apply.
Step 4 | If the angles are vertical, they are equal. The value of the given angle is the same as the value of the other angle. Go to Step 5. |
Step 5 | Write the final answer. | =