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

Two angles are complementary if their sum is 90 degrees. Given the measures of the angles are \( (2x)^\circ \) and \( (3x)^\circ \), we can set up the equation:

\[ 2x + 3x = 90 \]

This simplifies to:

\[ 5x = 90 \]

Now, divide both sides by 5:

\[ x = 18 \]

Now, we can find the measures of the two angles:

  1. \( 2x = 2 \times 18 = 36^\circ \)
  2. \( 3x = 3 \times 18 = 54^\circ \)

Therefore, the values are:

\( x = 18 \), \( (2x) = 36^\circ \), and \( (3x) = 54^\circ \).