Complementary angles are two angles that add up to 90 degrees. To solve for a missing complementary angle, use the following method:
Understanding Complementary Angles
- Definition: Complementary angles are a pair of angles whose measures sum to 90 degrees.
- Key Property: The sum of complementary angles is always 90°.
Solving for a Missing Complementary Angle
To find a missing complementary angle, follow these steps:
- Identify the Given Angle: Determine the measure of the angle that you already know.
- Subtract from 90 Degrees: Subtract the known angle from 90 degrees. The result will be the measure of the missing complementary angle.
- Verify: Check your answer by adding the two angle measures together. The sum should be 90 degrees.
Example:
Let's say one of the complementary angles is 70 degrees.
- The total is always 90 degrees.
- To find the other angle, subtract 70 degrees from 90 degrees, as demonstrated in the reference.
90 - 70 = 20 - Therefore, the missing complementary angle is 20 degrees.
- Verification:
70 + 20 = 90
General Formula
The formula to solve for complementary angles is:
Angle 1 + Angle 2 = 90°- If
Angle 1is known andAngle 2is the missing angle, then:
Angle 2 = 90° - Angle 1
Practical Insights
- Complementary angles are always less than 90 degrees.
- If the problem provides any angle larger than or equal to 90, it can't be a complementary angle.
- If one angle of a complementary pair is known, the other can always be determined with a simple calculation.
Solving Example Cases
| Given Angle | Missing Angle |
|---|---|
| 30° | 60° |
| 45° | 45° |
| 65° | 25° |
| 15° | 75° |
The reference explains, "So 90 degrees minus 70 degrees equals 20 degrees so x equals 20 degrees and let's double check 70 degrees what we were given plus that 20 degrees gives us 90 degrees again complementary angles add add" as an example, which showcases the process of subtracting a known angle from 90° to find the complementary angle.
