Question

c = (24x + 5)° and e = (28x - 7)°, find the measures of c and e.

Explanation:

Step1: Identify angle - relationship

Since \(m\parallel n\), \(\angle C\) and \(\angle E\) are corresponding angles, so \(\angle C=\angle E\).

Step2: Set up the equation

Set \(24x + 5=28x-7\).

Step3: Solve for \(x\)

Subtract \(24x\) from both sides: \(5 = 4x-7\).
Add 7 to both sides: \(12 = 4x\).
Divide both sides by 4: \(x = 3\).

Step4: Find the measure of \(\angle C\)

Substitute \(x = 3\) into the expression for \(\angle C\): \(C=24x + 5=24\times3+5=72 + 5=77^{\circ}\).

Step5: Find the measure of \(\angle E\)

Since \(\angle C=\angle E\), \(E = 77^{\circ}\).

Answer:

\(C = 77^{\circ}\), \(E = 77^{\circ}\)