Questions: What is the measure of angle CBE? 36° 72° 108° 144°

Transcript text: What is the measure of $\angle \mathrm{CBE} ?$ $36^{\circ}$ $72^{\circ}$ $108^{\circ}$ $144^{\circ}$

Solution

Step 1: Identify the Given Angles

The problem provides two angles:

Step 2: Use the Property of a Straight Line

Since $\angle CBA$ and $\angle BED$ are on a straight line, their sum is $180^\circ$ : $3x + 2x = 180^\circ$

Step 3: Solve for

x

Combine the terms and solve for $x$ : $5x = 180^\circ$ $x = \frac{180^\circ}{5}$ $x = 36^\circ$

Step 4: Calculate

\angle CBE

Substitute $x$ back into $\angle CBA$ : $\angle CBA = 3x = 3 \times 36^\circ = 108^\circ$

The measure of $\angle CBE$ is $108^\circ$ .

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