Question

midterm (chapters 4, 5, 6, 8.1, 8.2) question 41, 8.1.79. the angles are supplementary angles. determine the measures of ∠1 and ∠2. m∠1 = ☐°, and m∠2 = ☐°

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. So, \(x+(2x - 3)=180\).

Step2: Simplify the equation

Combine like - terms: \(x+2x-3 = 180\) becomes \(3x-3 = 180\).

Step3: Isolate the variable term

Add 3 to both sides of the equation: \(3x-3 + 3=180 + 3\), resulting in \(3x=183\).

Step4: Solve for x

Divide both sides by 3: \(x=\frac{183}{3}=61\).

Step5: Find the measure of ∠1

Substitute \(x = 61\) into the expression for ∠1 (\(2x-3\)): \(m\angle1=2\times61 - 3=122 - 3=119^{\circ}\).

Step6: Find the measure of ∠2

Substitute \(x = 61\) into the expression for ∠2 (\(x\)): \(m\angle2 = 61^{\circ}\).

Answer:

\(m\angle1 = 119^{\circ}\), and \(m\angle2 = 61^{\circ}\)