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Answer :
Final answer:
To prove E bisects ∠AEC given m∠AEB = 45° and ∠AEC is a right angle, we deduce m∠BEC must also be 45° so the angles sum to m∠AEC, which is 90°. This proves E bisects the angle as each adjacent angle measures 45°.
Explanation:
To prove that point E bisects ∠AEC in which m∠AEB = 45° and ∠AEC is a right angle, we can analyze the given angles.
Step 1: Recognize that ∠AEC being a right angle means m∠AEC = 90°.
Step 2: If E bisects ∠AEC, then m∠BEC would be equal to m∠AEB because a bisected angle is divided into two congruent angles.
Step 3: Since it is given that m∠AEB = 45°, for E to bisect ∠AEC, m∠BEC must also be 45° so that their sum equals to 90° which is the measure of a right angle.
This satisfies option (d): m∠BEC = 45°, meaning that the angle is indeed bisected.
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