Question

find the measure of ∠dpy. 3k + 49 3k + 53

Explanation:

Step1: Assume the angle - sum relationship

Since the sum of angles \(\angle DPY\) and \(\angle YPT\) is likely to be a known angle (if it's a right - angle or a straight - angle, assume it's a right - angle here, i.e., \(\angle DPT = 90^{\circ}\)), we have \((3k + 49)+(3k + 53)=90\).

Step2: Combine like terms

\[

$$\begin{align*} 3k+3k + 49+53&=90\\ 6k+102&=90 \end{align*}$$

\]

Step3: Solve for \(k\)

Subtract 102 from both sides: \(6k=90 - 102=- 12\). Then divide both sides by 6: \(k=\frac{-12}{6}=-2\).

Step4: Find the measure of \(\angle DPY\)

Substitute \(k = - 2\) into the expression for \(\angle DPY\) which is \(3k + 49\). So \(\angle DPY=3\times(-2)+49=-6 + 49 = 43^{\circ}\).

Answer:

\(43^{\circ}\)