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, \(x+(6x - 9)=180\).

Step2: Simplify the equation

Combine like - terms: \(x+6x-9 = 180\), which becomes \(7x-9 = 180\).

Step3: Isolate the variable term

Add 9 to both sides of the equation: \(7x-9 + 9=180 + 9\), resulting in \(7x=189\).

Step4: Solve for x

Divide both sides by 7: \(x=\frac{189}{7}=27\).

Step5: Find the measure of ∠1

Substitute \(x = 27\) into the expression for ∠1: \(m\angle1=6x - 9=6\times27-9=162 - 9 = 153^{\circ}\).

Step6: Find the measure of ∠2

Since \(x = 27\), \(m\angle2=x = 27^{\circ}\).

Answer:

\(m\angle1 = 153^{\circ}\), and \(m\angle2 = 27^{\circ}\)