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 \(m\parallel n\), angles \(C\) and \(E\) are corresponding angles, so \(C = E\).
\[24x + 5=28x - 7\]

Step2: Solve for \(x\)

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

Step3: Find the measure of angle \(C\)

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

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

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

Answer:

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