Question

Given: Ray E B bisects ∠AEC.

∠AED is a straight angle.

Prove: m∠AEB = 45°

A horizontal line has points A, E, D. 2 lines extend from point E. One line extends to point B and another extends to point C. Angle C E D is a right angle.
Complete the paragraph proof.

We are given that Ray E B bisects ∠AEC. From the diagram, ∠CED is a right angle, which measures
degrees. Since the measure of a straight angle is 180°, the measure of angle
must also be 90° by the
. A bisector cuts the angle measure in half. m∠AEB is 45°.

Answer 1

We are given that Ray EB bisects ∠AEC. From the diagram, ∠CED is a right angle, which measures 90 degrees. Since the measure of a straight angle is 180°, the measure of angle AEC must also be 90° by the Supplement (Linear Pair) Theorem (m∠AEC + m∠CED = 180°). A bisector cuts the angle measure in half. Therefore m∠AEB = 45°.