The measure of angle CBE is 72°.
Given:
[tex]m \angle ABC = 3x\\[/tex]
[tex]m \angle FED =2x[/tex]
Thus:
[tex]\angle CBE $ and $ \angle FED[/tex] are congruent angles as marked in the diagram given.
Therefore:
[tex]m \angle CBE = 2x[/tex]
[tex]m \angle CBE + m \angle ABC = 180^{\circ}[/tex] (angles on a straight line are supplementary).
Substitute
[tex]3x + 2x = 180[/tex]
Solve for x
[tex]5x = 180[/tex]
Divide both sides by 5
[tex]x = 36[/tex]
Find angle CBE
[tex]m \angle CBE = 2x[/tex]
Plug in the value of x
[tex]m \angle CBE = 2(36)\\m \angle CBE = 72^{\circ}[/tex]
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