Question
An angle is twice as large as the measure of its complement. find the two angles
Answers
Answered by
GPT-4o mini
Let the measure of the angle be \( x \) degrees. The measure of its complement will then be \( 90 - x \) degrees.
According to the problem, the angle is twice as large as its complement. This can be expressed with the equation:
\[
x = 2(90 - x)
\]
Now, let's solve for \( x \):
1. Distribute the 2 on the right side:
\[
x = 180 - 2x
\]
2. Add \( 2x \) to both sides to get all \( x \) terms on one side:
\[
x + 2x = 180
\]
3. Combine like terms:
\[
3x = 180
\]
4. Divide both sides by 3:
\[
x = 60
\]
Now that we found \( x \), the measure of the angle is \( 60 \) degrees.
To find the complement, substitute \( x \) back into the complement expression:
\[
90 - x = 90 - 60 = 30
\]
Thus, the two angles are:
- The angle: \( 60 \) degrees
- Its complement: \( 30 \) degrees
So the two angles are \( 60^\circ \) and \( 30^\circ \).
According to the problem, the angle is twice as large as its complement. This can be expressed with the equation:
\[
x = 2(90 - x)
\]
Now, let's solve for \( x \):
1. Distribute the 2 on the right side:
\[
x = 180 - 2x
\]
2. Add \( 2x \) to both sides to get all \( x \) terms on one side:
\[
x + 2x = 180
\]
3. Combine like terms:
\[
3x = 180
\]
4. Divide both sides by 3:
\[
x = 60
\]
Now that we found \( x \), the measure of the angle is \( 60 \) degrees.
To find the complement, substitute \( x \) back into the complement expression:
\[
90 - x = 90 - 60 = 30
\]
Thus, the two angles are:
- The angle: \( 60 \) degrees
- Its complement: \( 30 \) degrees
So the two angles are \( 60^\circ \) and \( 30^\circ \).