Question

19 multiple choice 5 points what is the measure of angle f? none of the above 79 degrees 159 degrees 111 degrees

Explanation:

Step1: Recall angle - sum property

The sum of angles around a point is 360 degrees. Also, vertical - angles are equal. But we can use the fact that the sum of angles in a linear - pair is 180 degrees. Angle \(e = 69^{\circ}\) and the angle adjacent to \(f\) and \(e\) forms a linear - pair with the 32 - degree angle.

Step2: Calculate the angle adjacent to \(f\)

The angle adjacent to \(f\) and \(e\) and the 32 - degree angle are supplementary. Let the angle adjacent to \(f\) be \(x\). Then \(x+32^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-32^{\circ}=148^{\circ}\).

Step3: Calculate angle \(f\)

We know that \(e + f+x=180^{\circ}\) (since they are angles on a straight - line). Substitute \(e = 69^{\circ}\) and \(x = 148^{\circ}\) into the equation: \(69^{\circ}+f + 148^{\circ}=180^{\circ}\). First, simplify the left - hand side: \(69^{\circ}+148^{\circ}=217^{\circ}\). Then \(f=180^{\circ}-(69^{\circ}+32^{\circ})\). \(f = 79^{\circ}\).

Answer:

B. 79 degrees