Question
An angle measures 6 degrees more than its complementary angle. What is the measure of each angle
Answers
GPT-4o mini
Let the measure of the complementary angle be \( x \). Since the angle in question measures 6 degrees more than its complementary angle, it can be expressed as \( x + 6 \).
We know that two angles are complementary if the sum of their measures is 90 degrees. Therefore, we can set up the equation:
\[
x + (x + 6) = 90
\]
Simplifying this equation gives:
\[
2x + 6 = 90
\]
Subtracting 6 from both sides:
\[
2x = 84
\]
Dividing both sides by 2:
\[
x = 42
\]
Now, we can find the measure of the other angle:
\[
x + 6 = 42 + 6 = 48
\]
Thus, the measures of the two angles are:
- The complementary angle: \( 42 \) degrees
- The angle that is 6 degrees more: \( 48 \) degrees
Therefore, the measures of the angles are:
- \( 42 \) degrees and \( 48 \) degrees.
We know that two angles are complementary if the sum of their measures is 90 degrees. Therefore, we can set up the equation:
\[
x + (x + 6) = 90
\]
Simplifying this equation gives:
\[
2x + 6 = 90
\]
Subtracting 6 from both sides:
\[
2x = 84
\]
Dividing both sides by 2:
\[
x = 42
\]
Now, we can find the measure of the other angle:
\[
x + 6 = 42 + 6 = 48
\]
Thus, the measures of the two angles are:
- The complementary angle: \( 42 \) degrees
- The angle that is 6 degrees more: \( 48 \) degrees
Therefore, the measures of the angles are:
- \( 42 \) degrees and \( 48 \) degrees.