# 9.3 Use properties of angles, triangles, and the pythagorean theorem  (Page 2/15)

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The next example will show how you can use the Problem Solving Strategy for Geometry Applications to answer questions about supplementary and complementary angles.

An angle measures $\text{40°}.$ Find its supplement, and its complement.

## Solution

 ⓐ Step 1. Read the problem. Draw the figure and label it with the given information. Step 2. Identify what you are looking for. Step 3. Name. Choose a variable to represent it. 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. ⓑ Step 1. Read the problem. Draw the figure and label it with the given information. Step 2. Identify what you are looking for. Step 3. Name. Choose a variable to represent it. 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. An angle measures $\text{25°}.$ Find its: supplement complement.

1. 155°
2. 65°

An angle measures $\text{77°}.$ Find its: supplement complement.

1. 103°
2. 13°

Did you notice that the words complementary and supplementary are in alphabetical order just like $90$ and $180$ are in numerical order?

Two angles are supplementary. The larger angle is $\text{30°}$ more than the smaller angle. Find the measure of both angles.

## Solution

 Step 1. Read the problem. Draw the figure and label it with the given information. Step 2. Identify what you are looking for. Step 3. Name. Choose a variable to represent it. The larger angle is 30° more than the smaller angle.  Step 4. Translate. Write the appropriate formula and substitute. Step 5. Solve the equation.       Step 6. Check:   Step 7. Answer the question. Two angles are supplementary. The larger angle is $\text{100°}$ more than the smaller angle. Find the measures of both angles.

40°, 140°

Two angles are complementary. The larger angle is $\text{40°}$ more than the smaller angle. Find the measures of both angles.

25°, 65°

## Use the properties of triangles

What do you already know about triangles? Triangle have three sides and three angles. Triangles are named by their vertices. The triangle    in [link] is called $\text{Δ}ABC,$ read ‘triangle $\text{ABC}$ ’. We label each side with a lower case letter to match the upper case letter of the opposite vertex. Δ A B C has vertices A , B , and C and sides a , b , and c .

The three angles of a triangle are related in a special way. The sum of their measures is $\text{180°}.$

$m\text{∠}A+m\text{∠}B+m\text{∠}C=\text{180°}$

## Sum of the measures of the angles of a triangle

For any $\text{Δ}ABC,$ the sum of the measures of the angles is $\text{180°}.$

$m\text{∠}A+m\text{∠}B+m\text{∠}C=\text{180°}$

The measures of two angles of a triangle are $\text{55°}$ and $\text{82°}.$ Find the measure of the third angle.

## Solution

 Step 1. Read the problem. Draw the figure and label it with the given information. Step 2. Identify what you are looking for. Step 3. Name. Choose a variable to represent it. Step 4. Translate. Write the appropriate formula and substitute. Step 5. Solve the equation.   Step 6. Check:  Step 7. Answer the question. The measures of two angles of a triangle are $\text{31°}$ and $\text{128°}.$ Find the measure of the third angle.

21°

A triangle has angles of $\text{49°}$ and $\text{75°}.$ Find the measure of the third angle.

56°

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