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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