Question

find the measure of ∠mpq.
(10x + 28)°
(52 - 2x)°
m∠mpq = □°

Explanation:

Step1: Identify angle - relationship

Assume \(LM\parallel NO\), then \(\angle MPQ\) and the angle \((52 - 2x)^{\circ}\) are corresponding angles. So \(10x + 28=52 - 2x\).

Step2: Solve for \(x\)

Add \(2x\) to both sides: \(10x+2x + 28=52-2x + 2x\), which gives \(12x+28 = 52\). Then subtract 28 from both sides: \(12x+28 - 28=52 - 28\), so \(12x=24\). Divide both sides by 12: \(x = 2\).

Step3: Find measure of \(\angle MPQ\)

Substitute \(x = 2\) into the expression for \(\angle MPQ\) (\(10x + 28\)). We get \(10\times2+28=20 + 28=48\).

Answer:

\(48\)