Two complementary angles have measures  (2x)° and (3x)° . What is the value of x and the two angle measures?(2 points)

x=___ , (2x)°=___ °, and (3x)°= ___

1 answer

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

\[ 2x + 3x = 90 \]

Combining like terms gives:

\[ 5x = 90 \]

Now, solving for \(x\):

\[ x = \frac{90}{5} = 18 \]

Now we can find the measures of the two angles:

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

\[ (2x)^\circ = 2(18)^\circ = 36^\circ \]

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

\[ (3x)^\circ = 3(18)^\circ = 54^\circ \]

So, the values are:

\[ x = 18, \quad (2x)^\circ = 36^\circ, \quad (3x)^\circ = 54^\circ \]

Final answer: \( x = 18, (2x)^\circ = 36^\circ, (3x)^\circ = 54^\circ \)