Recall that two angles are complementary if the sum of their measures is 90degrees.

Question

Find the measures of two complementary angles if one angle is 15degrees more than four times the other angle.

Answer 1

Let the measure of one angle be denoted as \( x \). According to the problem, the other angle is \( 4x + 15 \) degrees.

Since the two angles are complementary, their sum must equal 90 degrees:

\[ x + (4x + 15) = 90 \]

Now, simplify the equation:

\[ x + 4x + 15 = 90 \] \[ 5x + 15 = 90 \]

Next, subtract 15 from both sides:

\[ 5x = 90 - 15 \] \[ 5x = 75 \]

Now, divide by 5 to solve for \( x \):

\[ x = \frac{75}{5} = 15 \]

Now that we have the value of \( x \), we can find the measure of the other angle:

\[ 4x + 15 = 4(15) + 15 = 60 + 15 = 75 \]

Thus, the two complementary angles are:

\[ \text{First angle: } 15 \text{ degrees} \] \[ \text{Second angle: } 75 \text{ degrees} \]

Therefore, the measures of the two complementary angles are \( 15 \) degrees and \( 75 \) degrees.