Question

practice - angle pairs n - gen math® 8 1. angle e and angle f are complementary. if m∠e = 5x - 11 and x = 7, determine the measure of ∠f.

Explanation:

Step1: Find measure of ∠E

Substitute \(x = 7\) into \(m\angle E=5x - 11\).

$$m\angle E=5\times7 - 11=35 - 11 = 24^{\circ}$$

Step2: Use complementary - angle property

Since \(\angle E\) and \(\angle F\) are complementary, \(m\angle E+m\angle F = 90^{\circ}\). Then \(m\angle F=90^{\circ}-m\angle E\).

$$m\angle F=90 - 24=66^{\circ}$$

Answer:

\(66^{\circ}\)