Question

supplementary angles are two angles that have measures with a sum of 180°. angles 1 and 2 are supplementary and the measure of angle 2 is 20 degrees less than three times the measure of angle 1.
write a system of equations and use substitution to find the measures of angles 1 and 2.
100 characters remaining

Explanation:

Step1: Define variables and equations

Let \( m\angle1 = x \) and \( m\angle2 = y \). Since they are supplementary, \( x + y = 180^\circ \). Also, \( y = 3x - 20^\circ \) (angle 2 is 20° less than three times angle 1).

Step2: Substitute the second equation into the first

Substitute \( y = 3x - 20^\circ \) into \( x + y = 180^\circ \):
\( x + (3x - 20^\circ) = 180^\circ \)
Simplify: \( 4x - 20^\circ = 180^\circ \)
Add \( 20^\circ \) to both sides: \( 4x = 200^\circ \)
Divide by 4: \( x = 50^\circ \)

Step3: Find \( y \)

Substitute \( x = 50^\circ \) into \( y = 3x - 20^\circ \):
\( y = 3(50^\circ) - 20^\circ = 150^\circ - 20^\circ = 130^\circ \)

Answer:

The measure of angle 1 is \( 50^\circ \) and angle 2 is \( 130^\circ \). The system of equations is \(

$$\begin{cases} x + y = 180^\circ \\ y = 3x - 20^\circ \end{cases}$$

\) (where \( x = m\angle1 \), \( y = m\angle2 \)) and solving gives \( m\angle1 = 50^\circ \), \( m\angle2 = 130^\circ \).