Question

∠1 and ∠2 are supplementary angles. if m∠1 = (3x - 2)° and m∠2 = (x - 18)°, then find the measure of ∠2.

Explanation:

Step1: Use the property of supplementary angles

Supplementary angles sum to \(180^{\circ}\). So, \(m\angle1 + m\angle2=180^{\circ}\).
Substitute \(m\angle1=(3x - 2)^{\circ}\) and \(m\angle2=(x - 18)^{\circ}\) into the equation:
\((3x - 2)+(x - 18)=180\)

Step2: Simplify the left - hand side of the equation

Combine like terms: \(3x+x-2 - 18=180\), which gives \(4x-20 = 180\)

Step3: Solve for \(x\)

Add \(20\) to both sides of the equation: \(4x-20 + 20=180 + 20\), so \(4x=200\)
Divide both sides by \(4\): \(x=\frac{200}{4}=50\)

Step4: Find the measure of \(\angle2\)

Substitute \(x = 50\) into \(m\angle2=(x - 18)^{\circ}\)
\(m\angle2=(50-18)^{\circ}=32^{\circ}\)

Answer:

\(32^{\circ}\)