two are complementary angles are expressed in terms of (2x - 6) and (2x) write and solve an equation for x and give the measure of the two angles

Answer 1

Complementary angles are two angles whose measures add up to 90 degrees. Given the angles \( (2x - 6) \) and \( 2x \), we can set up the equation as follows:

\[ (2x - 6) + (2x) = 90 \]

Now, combine like terms:

\[ 2x - 6 + 2x = 90 \] \[ 4x - 6 = 90 \]

Next, add 6 to both sides of the equation:

\[ 4x - 6 + 6 = 90 + 6 \] \[ 4x = 96 \]

Now, divide both sides by 4 to solve for \( x \):

\[ x = \frac{96}{4} \] \[ x = 24 \]

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

1. First angle: \[ 2x - 6 = 2(24) - 6 = 48 - 6 = 42 \]

2. Second angle: \[ 2x = 2(24) = 48 \]

Thus, the two complementary angles are \( 42 \) degrees and \( 48 \) degrees.