Question

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, \(x+(2x - 6)=180\).

Step2: Simplify the equation

Combine like - terms: \(x+2x-6 = 180\) becomes \(3x-6 = 180\).
Add 6 to both sides: \(3x=180 + 6=186\).

Step3: Solve for x

Divide both sides of the equation \(3x = 186\) by 3. So, \(x=\frac{186}{3}=62\).

Step4: Find the measure of ∠1

Substitute \(x = 62\) into the expression for ∠1. Since \(m\angle1=2x - 6\), then \(m\angle1=2\times62-6=124 - 6=118^{\circ}\).

Step5: Find the measure of ∠2

Since \(m\angle2=x\), and \(x = 62\), then \(m\angle2 = 62^{\circ}\).

Answer:

\(m\angle1 = 118^{\circ}\), and \(m\angle2 = 62^{\circ}\)