Question

find the measure of \\( \angle ygt \\).

Explanation:

Step1: Set up the equation

Since \( \angle RGY = 90^{\circ}\), we have \((3f + 12)+(3f + 42)=90\).

Step2: Simplify the equation

Combine like - terms: \(6f+54 = 90\).
Subtract 54 from both sides: \(6f=90 - 54\), so \(6f = 36\).
Divide both sides by 6: \(f=\frac{36}{6}=6\).

Step3: Find the measure of \(\angle YGT\)

Substitute \(f = 6\) into \(3f + 42\).
\(3\times6+42=18 + 42=60\).

Answer:

\(60^{\circ}\)