Question

finding an angle measure. what is the measure of ∠cbe? (3x)° (2x)° 72° 108° 36° 144°

Explanation:

Step1: Use property of parallel - sided figure

In the figure, since \(CD\parallel AF\), the sum of the interior angles on the same - side of the transversal is \(180^{\circ}\). So, \(3x + 2x=180^{\circ}\).

Step2: Solve for \(x\)

Combining like terms in the equation \(3x + 2x = 180^{\circ}\), we get \(5x=180^{\circ}\). Then, \(x=\frac{180^{\circ}}{5}=36^{\circ}\).

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

\(\angle CBE = 3x\). Substitute \(x = 36^{\circ}\) into \(3x\), we have \(\angle CBE=3\times36^{\circ}=108^{\circ}\).

Answer:

\(108^{\circ}\)