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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 $\text{40\xb0}.$ Find ⓐ its supplement, and ⓑ its complement.
ⓐ  
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 $\text{25\xb0}.$ Find its: ⓐ supplement ⓑ complement.
An angle measures $\text{77\xb0}.$ Find its: ⓐ supplement ⓑ complement.
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 $\text{30\xb0}$ more than the smaller angle. Find the measure of both angles.
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 $\text{100\xb0}$ more than the smaller angle. Find the measures of both angles.
40°, 140°
Two angles are complementary. The larger angle is $\text{40\xb0}$ more than the smaller angle. Find the measures of both angles.
25°, 65°
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 $\text{\Delta}ABC,$ read ‘triangle $\text{ABC}$ ’. We label each side with a lower case letter to match the upper case letter of the opposite vertex.
The three angles of a triangle are related in a special way. The sum of their measures is $\text{180\xb0}.$
For any $\text{\Delta}ABC,$ the sum of the measures of the angles is $\text{180\xb0}.$
The measures of two angles of a triangle are $\text{55\xb0}$ and $\text{82\xb0}.$ Find the measure of the third angle.
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 $\text{31\xb0}$ and $\text{128\xb0}.$ Find the measure of the third angle.
21°
A triangle has angles of $\text{49\xb0}$ and $\text{75\xb0}.$ Find the measure of the third angle.
56°
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