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

Question

x= __, (2x)°= __° , and (3x)°= __°

Answer 1

Complementary angles are two angles whose measures add up to 90 degrees. Given that the two angles are (2x)° and (3x)°, we can set up the equation:

\[ 2x + 3x = 90 \]

Combining the terms gives us:

\[ 5x = 90 \]

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 angles:

1. For the angle \(2x\):

\[ 2x = 2 \times 18 = 36° \]

2. For the angle \(3x\):

\[ 3x = 3 \times 18 = 54° \]

Therefore, the values are:

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