Question

find the measures of the indicated angles, using the diagram below. c=(24x + 5)° and e=(28x - 7)°, find the measures of c and e. m||n enter the exact answers. c= e=

Explanation:

Step1: Identify angle - relationship

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

Step2: Set up equation

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

Step3: Solve for \(x\)

Subtract \(24x\) from both sides: \(5 = 4x-7\). Then add 7 to both sides: \(12 = 4x\). Divide both sides by 4, we get \(x = 3\).

Step4: Find 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 measure of \(\angle E\)

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

Answer:

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