Question

find the measure of each lettered angle

Explanation:

Step1: Find angle \(e\)

Since the sum of angles in a right - angled triangle - like situation (with a right angle of \(90^{\circ}\)) and an angle of \(64^{\circ}\), we use \(e = 90^{\circ}-64^{\circ}\).
\(e = 26^{\circ}\)

Step2: Find angle \(c\)

\(c\) and \(e\) are alternate interior angles (due to parallel lines). So \(c = e\).
\(c = 26^{\circ}\)

Step3: Find angle \(d\)

\(d\) and \(c\) are supplementary (linear pair). So \(d=180^{\circ}-c\).
\(d = 180^{\circ}-26^{\circ}=154^{\circ}\)

Step4: Find angle \(g\)

\(g\) and \(d\) are alternate interior angles (due to parallel lines). So \(g = d\).
\(g = 154^{\circ}\)

Step5: Find angle \(f\)

\(f\) and \(76^{\circ}\) are supplementary (linear pair). So \(f = 180^{\circ}-76^{\circ}\).
\(f = 104^{\circ}\)

Step6: Find angle \(h\)

\(h\) and \(f\) are alternate interior angles (due to parallel lines). So \(h = f\).
\(h = 104^{\circ}\)

Step7: Find angle \(k\)

\(k\) and \(76^{\circ}\) are vertical angles. So \(k = 76^{\circ}\)

Answer:

\(c = 26^{\circ}\), \(d = 154^{\circ}\), \(e = 26^{\circ}\), \(g = 154^{\circ}\), \(f = 104^{\circ}\), \(h = 104^{\circ}\), \(k = 76^{\circ}\)