Question

1. ∠efh and ∠hfi are complementary angles. if m∠efh = (2x + 2)° and m∠hfi = (x + 1)°, then what is m∠hfi? m∠hfi = 30°

Explanation:

Step1: Recall complementary angles sum

Complementary angles sum to \(90^\circ\). So, \(m\angle EFH + m\angle HFI = 90^\circ\).

Step2: Substitute angle expressions

Substitute \(m\angle EFH = (2x + 2)^\circ\) and \(m\angle HFI = (x + 1)^\circ\) into the equation: \((2x + 2) + (x + 1) = 90\).

Step3: Solve for x

Simplify the left side: \(3x + 3 = 90\). Subtract 3: \(3x = 87\). Divide by 3: \(x = 29\).

Step4: Find \(m\angle HFI\)

Substitute \(x = 29\) into \(m\angle HFI = (x + 1)^\circ\): \(29 + 1 = 30\). So, \(m\angle HFI = 30^\circ\).

Answer:

\(30^\circ\)