Question

what is the measure of ∠cbe? 36° 72° 108° 144°

Explanation:

Step1: Use the property of parallel lines

Since \(CD\parallel BE\) (assumed from the figure structure), \(\angle CBA+\angle BED = 180^{\circ}\) (same - side interior angles). But also, \(\angle CBA = 3x\) and \(\angle BED=2x\). So \(3x + 2x=180^{\circ}\).

Step2: Solve for \(x\)

Combine like terms: \(5x = 180^{\circ}\). Then \(x=\frac{180^{\circ}}{5}=36^{\circ}\).

Step3: Find \(\angle CBE\)

\(\angle CBE = 180^{\circ}-\angle CBA\). Substitute \(x = 36^{\circ}\), \(\angle CBA=3x = 3\times36^{\circ}=108^{\circ}\). So \(\angle CBE=180^{\circ}- 108^{\circ}=72^{\circ}\).

Answer:

B. \(72^{\circ}\)