Question

find the degree measures for the two distinct angles in the following figure. smaller angle: larger angle:

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, consecutive angles are supplementary. So, \((8x - 149)+(5x - 35)=180\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(8x+5x-149 - 35 = 180\), \(13x-184 = 180\).
Add \(184\) to both sides: \(13x=180 + 184\), \(13x=364\).
Divide both sides by \(13\): \(x=\frac{364}{13}=28\).

Step3: Find the measures of the angles

For the angle \((5x - 35)^{\circ}\), substitute \(x = 28\): \(5\times28-35=140 - 35=105^{\circ}\).
For the angle \((8x - 149)^{\circ}\), substitute \(x = 28\): \(8\times28-149=224 - 149 = 75^{\circ}\).

Answer:

Smaller Angle: \(75^{\circ}\)
Larger Angle: \(105^{\circ}\)