Question

find the measure of ∠ptd.

Explanation:

Step1: Set up equation

Since vertical - angles are equal, we set \(8h + 102=2h + 108\).
\[8h+102 = 2h + 108\]

Step2: Solve for h

Subtract \(2h\) from both sides: \(8h-2h+102=2h - 2h+108\), which simplifies to \(6h+102 = 108\). Then subtract 102 from both sides: \(6h+102 - 102=108 - 102\), getting \(6h=6\). Divide both sides by 6: \(h = 1\).
\[

$$\begin{align*} 6h&=6\\ h&=1 \end{align*}$$

\]

Step3: Find measure of ∠PTD

Substitute \(h = 1\) into the expression for ∠PTD (\(8h + 102\)). So \(8\times1+102=8 + 102=110\).
\[8h+102=8\times1 + 102=110\]

Answer:

\(110^{\circ}\)