Question

Given: ray e b bisects ∠aec. ∠aed is a straight angle. prove: m∠aeb = 45°

Answer 1

Given that ray EB bisects angle AEC and angle AED is a straight angle, we need to prove that angle AEB measures 45 degrees. However, after applying the given information and using the properties of angles, we find that angle AEB measures 0 degrees rather than 45 degrees. Therefore, the claim is not true.

Step-by-step explanation:

Given that ray EB bisects angle AEC and angle AED is a straight angle, we need to prove that angle AEB measures 45 degrees.

1. Since ray EB bisects angle AEC, we can conclude that angle AEB is equal to angle BEC.
2. Since angle AED is a straight angle, it measures 180 degrees.
3. Using the fact that the angles of a triangle add up to 180 degrees, we can write the equation: angle AEB + angle BEC + angle AED = 180 degrees.
4. Substituting angle AED = 180 degrees and angle AEB = angle BEC, we get: angle AEB + angle AEB + angle AED = 180 degrees.
5. Simplifying the equation, we obtain: 2(angle AEB) + 180 degrees = 180 degrees.
6. Subtracting 180 degrees from both sides, we find: 2(angle AEB) = 0 degrees.
7. Dividing both sides by 2, we get: angle AEB = 0 degrees/2 = 0 degrees.
8. Therefore, angle AEB measures 0 degrees, and not 45 degrees as we need to prove. Hence, the claim is not true.