Question

1. examine the diagram below.

(figure is not drawn to scale.)
what are the measures of the two angles in the diagram?
a. 50° and 150°
b. 65° and 115°
c. 80° and 100°
d. 75° and 105°

Explanation:

Step1: Set up the equation

Since the two angles form a linear pair, their sum is \(180^{\circ}\). So, \((30x - 15)+(20x - 5)=180\).

Step2: Simplify the equation

Combine like - terms: \(30x+20x-15 - 5=180\), which gives \(50x-20 = 180\).

Step3: Solve for \(x\)

Add \(20\) to both sides: \(50x=180 + 20=200\). Then divide by \(50\): \(x=\frac{200}{50}=4\).

Step4: Find the measures of the angles

For the first angle: \(30x-15\), substitute \(x = 4\). \(30\times4-15=120 - 15=105^{\circ}\).
For the second angle: \(20x-5\), substitute \(x = 4\). \(20\times4-5=80 - 5=75^{\circ}\).

Answer:

D. \(75^{\circ}\) and \(105^{\circ}\)