Question

finding an angle measure
what is the measure of $angle cbe$
$circ$ $36^circ$
$circ$ $72^circ$
$circ$ $108^circ$
$circ$ $144^circ$
$(3x)^circ$
$(2x)^circ$

Explanation:

Step1: Use paralleloragram angle property

Since $BC \parallel DE$, consecutive interior angles are supplementary, and $\angle CBE + (2x)^\circ = 180^\circ$. Also, $(3x)^\circ + \angle CBE = 180^\circ$, so $3x = 180 - \angle CBE$ and $2x = 180 - \angle BED$, with $\angle CBE + \angle BED = 180^\circ$. Alternatively, use the fact that same-side exterior angles for parallel lines satisfy $3x + 2x = 180$.
$$3x + 2x = 180$$

Step2: Solve for x

Combine like terms and isolate x.
$$5x = 180 \implies x = \frac{180}{5} = 36$$

Step3: Calculate $\angle CBE$

$\angle CBE$ is supplementary to $(3x)^\circ$, so $\angle CBE = 180 - 3x$.
$$\angle CBE = 180 - 3(36) = 180 - 108 = 72$$

Answer:

72°