Using Properties of Angles to Solve Problems
Learning Outcomes
- Find the supplement of an angle
- Find the complement of an angle

is the angle with vertex at .
We measure angles in degrees, and use the symbol to represent degrees. We use the abbreviation to for the measure of an angle. So if is , we would write .
If the sum of the measures of two angles is , then they are called supplementary angles. In the images below, each pair of angles is supplementary because their measures add to . Each angle is the supplement of the other.
The sum of the measures of supplementary angles is .



Supplementary and Complementary Angles
If the sum of the measures of two angles is , then the angles are supplementary.If angle and angle are supplementary, then .
If the sum of the measures of two angles is , then the angles are complementary.If angle and angle are complementary, then .
Use a Problem Solving Strategy for Geometry Applications.
- Read the problem and make sure you understand all the words and ideas. Draw a figure and label it with the given information.
- Identify what you are looking for.
- Name what you are looking for and choose a variable to represent it.
- Translate into an equation by writing the appropriate formula or model for the situation. Substitute in the given information.
- Solve the equation using good algebra techniques.
- Check the answer in the problem and make sure it makes sense.
- Answer the question with a complete sentence.
example
An angle measures . 1. Find its supplement 2. Find its complement Solution1. | |
Step 1. Read the problem. Draw the figure and label it with the given information. | ![]() |
Step 2. Identify what you are looking for. | The supplement of a angle. |
Step 3. Name. Choose a variable to represent it. | Let the measure of the supplement. |
Step 4. Translate. Write the appropriate formula for the situation and substitute in the given information. | |
Step 5. Solve the equation. | |
Step 6. Check: | |
Step 7. Answer the question. | The supplement of the angle is . |
2. | ||
Step 1. Read the problem. Draw the figure and label it with the given information. | ![]() |
|
Step 2. Identify what you are looking for. |
|
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Step 3. Name. Choose a variable to represent it. | Let the measure of the complement. | |
Step 4. Translate. Write the appropriate formula for the situation and substitute in the given information. | ||
Step 5. Solve the equation. | ||
Step 6. Check: | ||
Step 7. Answer the question. | The complement of the angle is . |
try it
[ohm_question]146495[/ohm_question]Exercises
Two angles are supplementary. The larger angle is more than the smaller angle. Find the measure of both angles.Answer: Solution:
Step 1. Read the problem. Draw the figure and label it with the given information. | ![]() |
Step 2. Identify what you are looking for. | The measures of both angles. |
Step 3. Name. Choose a variable to represent it. The larger angle is 30° more than the smaller angle. | Let measure of smaller angle measure of larger angle |
Step 4. Translate. Write the appropriate formula and substitute. | |
Step 5. Solve the equation. | measure of smaller angle. measure of larger angle. |
Step 6. Check: | |
Step 7. Answer the question. | The measures of the angle are and . |
try it
[ohm_question]146496[/ohm_question] [ohm_question]146497[/ohm_question]Contribute!
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