Question

find the measure of ∠mpo. m∠mpo = °

Explanation:

Step1: Set up equation using vertical - angle property

Since vertical angles are equal, we set \(8x - 5=65 - 2x\).

Step2: Solve for \(x\)

Add \(2x\) to both sides: \(8x+2x - 5=65-2x + 2x\), which simplifies to \(10x-5 = 65\). Then add 5 to both sides: \(10x-5 + 5=65 + 5\), getting \(10x=70\). Divide both sides by 10: \(x = 7\).

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

Substitute \(x = 7\) into the expression for \(\angle MPO\) which is \(8x-5\). So \(m\angle MPO=8\times7 - 5=56 - 5=51\).

Answer:

51