Question

1. ∠e and ∠f are supplementary. if m∠e = (9x - 38)° and m∠f = (2x + 42)°, find m∠f type a response

Explanation:

Step1: Recall supplementary angles property

Supplementary angles add up to \(180^\circ\). So, \(m\angle E + m\angle F=180^\circ\).
Substitute \(m\angle E=(9x - 38)^\circ\) and \(m\angle F=(2x + 42)^\circ\) into the equation:
\((9x - 38)+(2x + 42)=180\)

Step2: Simplify and solve for x

Combine like terms:
\(9x+2x-38 + 42=180\)
\(11x + 4=180\)
Subtract 4 from both sides:
\(11x=180 - 4\)
\(11x=176\)
Divide both sides by 11:
\(x=\frac{176}{11}=16\)

Step3: Find \(m\angle F\)

Substitute \(x = 16\) into the expression for \(m\angle F=(2x + 42)^\circ\):
\(m\angle F=2(16)+42\)
\(m\angle F=32 + 42\)
\(m\angle F = 74^\circ\)

Answer:

\(74^\circ\)