What are the two angle measures of complementary angles expressed as 3x°

and (2x−5)°
?(1 point)

A. 21° and 69°

B. 19° and 71°

C. 30° and 60°

D. 33° and 57°

1 answer

Complementary angles are two angles whose measures add up to 90 degrees. Given the angles as \(3x^\circ\) and \((2x - 5)^\circ\), we can set up the equation:

\[ 3x + (2x - 5) = 90 \]

Now, let's simplify the equation:

\[ 3x + 2x - 5 = 90 \] \[ 5x - 5 = 90 \] \[ 5x = 90 + 5 \] \[ 5x = 95 \] \[ x = 19 \]

Now, we can find the measures of the angles:

  1. For \(3x^\circ\):

\[ 3x = 3(19) = 57^\circ \]

  1. For \((2x - 5)^\circ\):

\[ 2x - 5 = 2(19) - 5 = 38 - 5 = 33^\circ \]

The two angles are \(57^\circ\) and \(33^\circ\). Thus, the two angle measures are:

D. 33° and 57°.