Question

∠1 and ∠2 are supplementary angles. if m∠1 = (x - 23)° and m∠2 = (x - 17)°, 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 \(m\angle1=(x - 23)^{\circ}\) and \(m\angle2=(x - 17)^{\circ}\) into the equation: \((x - 23)+(x - 17)=180\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(x+x-23 - 17=180\), which simplifies to \(2x-40 = 180\).

Step3: Solve for \(x\)

Add \(40\) to both sides: \(2x-40 + 40=180 + 40\), so \(2x=220\).
Divide both sides by \(2\): \(x=\frac{220}{2}=110\).

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

Substitute \(x = 110\) into \(m\angle2=(x - 17)^{\circ}\). Then \(m\angle2=(110-17)^{\circ}\).

Answer:

\(93^{\circ}\)