Question

supplementary angles are two angles that have measures with a sum of 180 degrees. angles 1 and 2 are supplementary and the measure of angle 2 is 20 degrees less than three times the measure of angle 1. find the measures of angles 1 and 2 given the hint. hint: x is angle 1, y is angle 2. x+y=180 and y=3x-20.

Explanation:

Step1: Substitute \( y = 3x - 20 \) into \( x + y = 180 \)

We know the two equations are \( x + y = 180 \) and \( y = 3x - 20 \). Substituting the second equation into the first gives \( x+(3x - 20)=180 \).

Step2: Simplify and solve for \( x \)

Simplify the left - hand side of the equation: \( x + 3x-20=180 \), which combines to \( 4x-20 = 180 \). Add 20 to both sides: \( 4x=180 + 20=200 \). Then divide both sides by 4: \( x=\frac{200}{4}=50 \).

Step3: Solve for \( y \)

Substitute \( x = 50 \) into the equation \( y = 3x-20 \). So \( y=3\times50 - 20=150 - 20 = 130 \).

Answer:

The measure of angle 1 (x) is 50 degrees and the measure of angle 2 (y) is 130 degrees.