Question

finding an angle measure
what is the measure of \\( \angle cbe \\)?
\\( 36 ^ { \circ } \\)
\\( 72 ^ { \circ } \\)
\\( 108 ^ { \circ } \\)
\\( 144 ^ { \circ } \\)

Explanation:

Step1: Use the property of parallel lines

Since \(CD\parallel BE\) (assuming \(CD\) and \(BE\) are parallel as it's a parallelogram - like figure in the context of angle - measure problems), the sum of \(\angle CBA=(3x)^{\circ}\) and \(\angle DEB=(2x)^{\circ}\) is \(180^{\circ}\) (consecutive interior angles). So, \(3x + 2x=180\).

Step2: Solve for \(x\)

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

Step3: Find \(\angle CBE\)

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

Answer:

\(72^{\circ}\)