We are given that m∠AEB = 45° and ∠AEC is a right angle. The measure of ∠AEC is 90° by the definition of a right angle. Applying
the gives m∠AEB + m∠BEC = m∠AEC. Applying the substitution property gives 45° + m∠BEC = 90°. The subtraction property can be used to find m∠BEC = 45°, so ∠BEC ≅ ∠AEB because they have the same measure. Since divides ∠AEC into two congruent angles, it is the angle bisector.
2 answers:
Answer:
The proof is given below.
Step-by-step explanation:
Given m∠AEB = 45° and ∠AEC is a right angle. we have to prove that EB divides ∠AEC into two congruent angles, it is the angle bisector.
Given ∠AEC=90° (Given)
∠AEC=∠AEB+∠BEC
⇒ 90° = 45° +∠BEC (Substitution Property)
By subtraction property of equality
⇒ ∠BEC = 90° - 45° = 45°
Hence, both angles becomes equal gives ∠AEB≅∠BEC
Since EB divides ∠AEC into two congruent angles, ∴ EB is the angle bisector.
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Applying the angle addition postulate, the measure of angle RST is: 66°.
<h3>What is the Angle Addition Postulate?</h3>If two angles share a common vertex and a common side, they are adjacent angles that form a larger angle. According to the angle addition postulate, the sum of these two adjacent angles will give a sum that is equal to the measure of the larger angle they both form.
We know the following:
Measure of angle RSU = 43º
Measure of angle UST = 23º
In the diagram given, angle RSU and angle UST are adjacent angles that form a larger angle, angle RST.
Therefore, based on the angle addition postulate, the measure of angle RST = sum of the measures of angles RSU and UST.
Therefore, we would have:
m∠RST = m∠RSU + m∠UST
Substitute
m∠RST = 43 + 23
m∠RST = 66°
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