The measure of an angle is 12 less than twice the measure of its complement. What is the measure of the angle?(1 point)

Question

Responses

39
39

84
84

116
116

56

Answer 1

Let the measure of the angle be \( x \). The complement of the angle is \( 90 - x \).

According to the problem, the measure of the angle is 12 less than twice the measure of its complement. This can be expressed with the equation:

\[ x = 2(90 - x) - 12 \]

Now, let's solve for \( x \):

1. Distribute on the right side: \[ x = 180 - 2x - 12 \] \[ x = 168 - 2x \]

2. Now, add \( 2x \) to both sides: \[ x + 2x = 168 \] \[ 3x = 168 \]

3. Divide both sides by 3: \[ x = \frac{168}{3} = 56 \]

The measure of the angle is \( 56 \).

Therefore, the correct response is 56.