What is the complement of a 45 degree angle?
Understand the Problem
The question is asking for the measure of the complement of a 45 degree angle. The complement of an angle is defined as what, when added to the angle, equals 90 degrees. Therefore, we need to subtract 45 from 90 to find the complement.
Answer
$45^\circ$
Answer for screen readers
The measure of the complement of a 45 degree angle is $45^\circ$.
Steps to Solve
-
Identify the given angle
The problem states that the angle we are working with is 45 degrees. -
Understanding the complement concept
The complement of an angle is found by subtracting the angle from 90 degrees. -
Set up the equation
To find the complement, we can write the equation as:
$$ \text{Complement} = 90^\circ - \text{Angle} $$ -
Substituting the values
Insert the known angle into the equation:
$$ \text{Complement} = 90^\circ - 45^\circ $$ -
Perform the subtraction
Calculate the complement:
$$ \text{Complement} = 45^\circ $$
The measure of the complement of a 45 degree angle is $45^\circ$.
More Information
The concept of complementary angles is often used in geometry, particularly in right triangles where the angles are associated with 90-degree angles. The two angles are a pair that completes the right angle.
Tips
- A common mistake is to confuse complementary angles with supplementary angles, which add up to 180 degrees instead of 90 degrees. To avoid this, always remember the definitions clearly.
