Question

find the measure of the missing angles.
answer attempt 1 out of 2
d = e = f =

Explanation:

Step1: Find \(d\)

Vertical angles are equal. The angle \(d\) and the angle composed of \(69^{\circ}\) and \(e\) (but we can also note that \(d = 69^{\circ}+ 32^{\circ}\) by the property of angles around a point where two lines intersect and we consider the non - overlapping angles.
\(d=69 + 32\)
\(d = 101^{\circ}\)

Step2: Find \(e\)

Complementary angles (since the vertical line and the other lines form right - angle - like relationships in terms of angle sums. The sum of angles on a straight line is \(180^{\circ}\). For the vertical line and the two adjacent angles \(69^{\circ}\) and \(e\), we know that \(e=90 - 69\) (assuming the vertical line is a straight line split into two parts by the other line.
\(e = 21^{\circ}\)

Step3: Find \(f\)

\(f\) and \(69^{\circ}+e\) are vertical angles. Also, using the sum of angles on a straight line. Since \(d + f=180^{\circ}\) (linear pair), and \(d = 101^{\circ}\), then \(f=180 - 101\)
\(f=79^{\circ}\)

Answer:

\(d = 101^{\circ}\), \(e = 21^{\circ}\), \(f = 79^{\circ}\)