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°.

Step-by-step explanation:

Given: Ray EB bisects <AEC

          <AED is a straight angle.

A bisector is a line that divides a segment or an angle into two equal parts.

m<AED = (measure of angle at a point on a straight line)

It can be observed that,

m<CED ≅ (meaning of right angle)

Thus,

m<CED ≅ m<AEC ≅ (congruent property)

So that,

m<CED + m<AEC ≅ m<AED ≅ (sum of angles at a point on a straight line)

Therefore, with ray EB;

m<AEB   (bisector property)

m<AEB ≅ m<BEC ≅ (congruence angle property)

So that,

m<AEB + m<BEC ≅ (complimentary angle property)

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step-by-step explanation:

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