Understanding Complementary Angles
Complementary angles are two angles that add up to 90 degrees. To find the two angles when given their difference, we can set up equations based on the information provided.
Setting Up the Problem
1. Let the two angles be A and B.
2. According to the problem:
- A + B = 90 degrees (since they are complementary)
- A - B = 18 degrees (the difference between the angles)
Solving the Equations
To solve the equations, we can use the following steps:
- From the first equation (A + B = 90), we can express B in terms of A:
B = 90 - A
- Substitute B in the second equation (A - B = 18):
A - (90 - A) = 18
- Simplifying this gives:
2A - 90 = 18
- Solving for A:
2A = 18 + 90
2A = 108
A = 54 degrees
- Now, substituting A back to find B:
B = 90 - A
B = 90 - 54
B = 36 degrees
Final Angles
- The two complementary angles are:
- Angle A = 54 degrees
- Angle B = 36 degrees
Thus, the two complementary angles that differ by 18 degrees are 54 degrees and 36 degrees.