Question

∠1 and ∠2 are supplementary angles. if m∠1 = (3x + 23)° and m∠2 = (4x - 4)°, then find the measure of ∠1.

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \((3x + 23)+(4x - 4)=180\).

Step2: Simplify the equation

Combine like - terms: \(3x+4x+23 - 4=180\), which gives \(7x+19 = 180\).

Step3: Solve for \(x\)

Subtract \(19\) from both sides: \(7x=180 - 19=161\). Then divide by \(7\): \(x=\frac{161}{7}=23\).

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

Substitute \(x = 23\) into \(m\angle1=(3x + 23)^{\circ}\). So, \(m\angle1=3\times23+23=(3 + 1)\times23=4\times23 = 92^{\circ}\).

Answer:

\(92^{\circ}\)