Question

find the measure of the missing angles.

Explanation:

Step1: Use angle - sum property of a straight - line

A straight - line has an angle of 180°. For the angle with 122° and \(d\) on a straight - line, we have \(d + 122^{\circ}=180^{\circ}\).
So, \(d=180^{\circ}- 122^{\circ}=58^{\circ}\).

Step2: Use angle - sum property for adjacent angles

We know that \(d\) and the 24° angle and another angle (let's call it \(x\)) form a straight - line. So \(x = 180^{\circ}-(d + 24^{\circ})\). Substituting \(d = 58^{\circ}\), we get \(x=180^{\circ}-(58^{\circ}+24^{\circ})=98^{\circ}\).

Step3: Use vertical - angle property

Vertical angles are equal. The angle \(e\) and the angle adjacent to the 24° and \(d\) (which we found as 98°) are vertical angles. So \(e = 180^{\circ}-98^{\circ}=82^{\circ}\).

Step4: Use vertical - angle property for \(f\)

Since \(f\) and \(e\) are vertical angles, \(f = e=82^{\circ}\).

Answer:

\(d = 58^{\circ}\), \(e = 82^{\circ}\), \(f = 82^{\circ}\)