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 considered complementary if their measures add up to 90 degrees. In this case, we have the two angles as \( (2x)^\circ \) and \( (3x)^\circ \).

We can set up the equation:

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

Combining the terms, we get:

\[ 5x = 90 \]

Now, we can solve for \( x \):

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

Now that we have the value of \( x \), we can find the measures of the two angles:

  1. For the angle \( (2x)^\circ \): \[ 2x = 2(18) = 36^\circ \]

  2. For the angle \( (3x)^\circ \): \[ 3x = 3(18) = 54^\circ \]

Therefore, the results are:

  • \( x = 18 \)
  • \( (2x)^\circ = 36^\circ \)
  • \( (3x)^\circ = 54^\circ \)

So the final answer is: \( x = 18 \), \( (2x)^\circ = 36^\circ \), and \( (3x)^\circ = 54^\circ \).