Question

for each of the following problems, write an equation and solve. 1. the measure of one angle is thirteen less than five times the measure of another angle. the sum of the measures of the two angles is 140°. determine the measure of each angle in degrees.

Explanation:

Step1: Define variables

Let the measure of one angle be \( x \) degrees. Then the measure of the other angle is \( 5x - 13 \) degrees (since it is thirteen less than five times the first angle).

Step2: Set up the equation

The sum of the two angles is \( 140^\circ \), so we can write the equation:
\( x + (5x - 13) = 140 \)

Step3: Solve the equation

First, simplify the left side:
\( x + 5x - 13 = 140 \)
\( 6x - 13 = 140 \)

Then, add 13 to both sides:
\( 6x - 13 + 13 = 140 + 13 \)
\( 6x = 153 \)

Next, divide both sides by 6:
\( x = \frac{153}{6} = 25.5 \)

Step4: Find the other angle

Now that we know \( x = 25.5 \), we can find the other angle:
\( 5x - 13 = 5(25.5) - 13 = 127.5 - 13 = 114.5 \)

Answer:

The measures of the two angles are \( 25.5^\circ \) and \( 114.5^\circ \).