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, \(x+(6x - 23)=180\).

Step2: Simplify the equation

Combine like - terms: \(x+6x-23 = 180\), which gives \(7x-23 = 180\).

Step3: Solve for \(x\)

Add 23 to both sides of the equation: \(7x=180 + 23\), so \(7x=203\). Then divide both sides by 7: \(x=\frac{203}{7}=29\).

Step4: Find the measure of \(\angle1\)

Substitute \(x = 29\) into the expression for \(\angle1\): \(m\angle1=6x-23=6\times29-23=174 - 23=151^{\circ}\).

Step5: Find the measure of \(\angle2\)

Since \(x = 29\), \(m\angle2=x = 29^{\circ}\).

Answer:

\(m\angle1 = 151^{\circ}\), \(m\angle2 = 29^{\circ}\)