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)
Responses

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

4x°−3°=90°
left parenthesis 4 x minus 3 right parenthesis degrees equals 90 degrees

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

2x°−3°=90°

1 answer

If the angles are complementary, their measures add up to 90 degrees. Given the measures of the two angles as \((x - 6)^\circ\) and \((3x + 3)^\circ\), we can set up the following equation:

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

Combining the terms, we get:

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

Thus, we can rewrite the equation as:

\[ 4x - 3 = 90 \]

Since this is the setup we derived from the relationship of complementary angles, the correct simplified equation for the angles is:

\[ 4x - 3 = 90° \]

So, the correct response from your options is:

4x°−3°=90° (left parenthesis 4 x minus 3 right parenthesis degrees equals 90 degrees)