Question

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

4x°−3°=90°
4 x degrees minus 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

2x°+3°=90°

Answer 1

Complementary angles are two angles whose measures add up to 90 degrees. Given the measures of the angles as \((x-6)°\) and \((3x+3)°\), we can set up the equation:

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

Now, let's simplify this:

1. Combine like terms:
\[
x + 3x - 6 + 3 = 90
\]
This simplifies to:
\[
4x - 3 = 90
\]

2. Finally, we can express this as:
\[
4x - 3° = 90°
\]

So the correct simplified equation for the angles is:

\[
4x - 3° = 90°
\]

Hence, the correct choice is:

**4x°−3°=90°**