Question

find the measure of the supplementary angles with measures 3x + 1 and 2x + 4 degrees.
a. 106° and 74°
b. 76° and 104°
c. 91° and 89°
d. 121° and 59°

Explanation:

Step1: Set up the equation for supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \((3x + 1)+(2x + 4)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(3x+2x + 1 + 4=180\), which gives \(5x+5 = 180\).

Step3: Solve for \(x\)

Subtract \(5\) from both sides: \(5x=180 - 5=175\). Then divide by \(5\): \(x=\frac{175}{5}=35\).

Step4: Find the measures of the angles

For the first angle: \(3x + 1=3\times35+1=105 + 1=106^{\circ}\).
For the second angle: \(2x + 4=2\times35+4=70+4=74^{\circ}\).

Answer:

A. \(106^{\circ}\) and \(74^{\circ}\)