Question

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

Explanation:

Step1: Assume lines LM and NO are parallel.

Since the angles \((10x + 28)^{\circ}\) and \((52-2x)^{\circ}\) are corresponding angles (assuming \(LM\parallel NO\)), they are equal. So we set up the equation \(10x + 28=52 - 2x\).

Step2: Solve the equation for \(x\).

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

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

Substitute \(x = 2\) into the expression for \(\angle MPQ\) which is \(10x+28\). So \(m\angle MPQ=10\times2 + 28=20 + 28=48^{\circ}\).

Answer:

\(48\)