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

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

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Solution Steps

Step 1: Identify the Given Angles

The problem provides two angles:

  • Angle \( \angle CBA = 3x \)
  • Angle \( \angle BED = 2x \)
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 \( \angle CBA \): \[ \angle CBA = 3x = 3 \times 36^\circ = 108^\circ \]

Final Answer

The measure of \( \angle CBE \) is \( 108^\circ \).

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