A figure shows two adjacent angles with measures (x−6)° and (3x+3)° . If the angles are complementary, what is the simplified equation for the angles?(1 point)

Question

Responses

2x°+3°=90°
2 x degrees plus 3 degrees is equal to 90 degrees - no response given

2x°−3°=90°
2 x degrees minus 3 degrees is equal to 90 degrees - incorrect

4x°+3°=90°
4 x degrees plus 3 degrees is equal to 90 degrees - no response given

4x°−3°=90°

Answer 1

Two angles are complementary when the sum of their measures equals 90 degrees. Given the measures of the angles as \( (x - 6)^\circ \) and \( (3x + 3)^\circ \), we can set up the equation as follows:

\[ (x - 6) + (3x + 3) = 90 \]

Now, simplify the left side of the equation:

\[ x - 6 + 3x + 3 = 90 \] \[ 4x - 3 = 90 \]

Now, we can isolate \( 4x \) by adding 3 to both sides:

\[ 4x = 90 + 3 \] \[ 4x = 93 \]

The simplified equation representing the relationship between the angles is:

\[ 4x - 3 = 90 \]

Therefore, the correct response is:

4x°−3°=90°.