A figure shows two adjacent angles with measures (x−6)°

Question

and (3x+3)°
. If the angles are complementary, what is the simplified equation for the angles?(1 point)
Responses

2x°−3°=90°
left parenthesis 2 x minus 3 right parenthesis degrees equals 90 degrees

4x°+3°=90°
left parenthesis 4 x plus 3 right parenthesis degrees equals 90 degrees

2x°+3°=90°
left parenthesis 2 x plus 3 right parenthesis degrees equals 90 degrees

4x°−3°=90

Answer 1

Two angles are complementary if their measures add up to \( 90^\circ \). In this case, the measures of the angles are given as \( (x - 6)^\circ \) and \( (3x + 3)^\circ \).

To set up the equation for these two angles being complementary, we can write:

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

Now, let's simplify the left side:

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

This means the simplified equation for the angles, combining the measures, would be:

\[ 4x - 3 = 90 \]

Hence, the correct response is:

4x°−3°=90 (or \(4x - 3 = 90\)).