Question

find the measure of ∠tym.

Explanation:

Step1: Set up the equation

Since \(\angle TYM\) and its adjacent angle form a linear pair (sum to \(180^{\circ}\)), we have \((8c + 22)+(3c + 81)=180\).

Step2: Simplify the equation

Combine like terms: \(8c+3c+22 + 81=180\), which gives \(11c+103 = 180\).

Step3: Solve for \(c\)

Subtract \(103\) from both sides: \(11c=180 - 103\), so \(11c=77\). Then divide by \(11\): \(c = 7\).

Step4: Find \(\angle TYM\)

Substitute \(c = 7\) into \(8c + 22\): \(8\times7+22=56 + 22=78\).

Answer:

\(78^{\circ}\)