Question

∠1 and ∠2 are supplementary angles. if m∠1 = (3x - 11)° and m∠2 = (5x - 9)°, then find the measure of ∠1.

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(3x - 11)^{\circ}\) and \(m\angle2=(5x - 9)^{\circ}\) into the equation:
\((3x - 11)+(5x - 9)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms:
\(3x+5x-11 - 9=180\)
\(8x-20 = 180\)

Step3: Solve for \(x\)

Add \(20\) to both sides of the equation:
\(8x-20 + 20=180 + 20\)
\(8x=200\)
Divide both sides by \(8\):
\(x=\frac{200}{8}=25\)

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

Substitute \(x = 25\) into \(m\angle1=(3x - 11)^{\circ}\)
\(m\angle1=(3\times25-11)^{\circ}=(75 - 11)^{\circ}\)
\(m\angle1 = 64^{\circ}\)

Answer:

\(64^{\circ}\)