Question

1. ∠e and ∠f are complementary. if m∠e=(8x - 29) and m∠f=(3x + 53), find x and m ∠f.

Explanation:

Step1: Recall complementary - angle property

Complementary angles sum to 90 degrees. So, \(m\angle E+m\angle F = 90\). Substitute the given expressions for \(m\angle E\) and \(m\angle F\): \((8x - 29)+(3x + 53)=90\).

Step2: Combine like - terms

\(8x+3x-29 + 53=90\), which simplifies to \(11x+24 = 90\).

Step3: Solve for x

Subtract 24 from both sides: \(11x=90 - 24\), so \(11x=66\). Then divide both sides by 11: \(x=\frac{66}{11}=6\).

Step4: Find \(m\angle F\)

Substitute \(x = 6\) into the expression for \(m\angle F\): \(m\angle F=3x + 53\). So \(m\angle F=3\times6+53\). First, calculate \(3\times6 = 18\), then \(18+53=71\).

Answer:

\(x = 6\), \(m\angle F=71^{\circ}\)