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1. Find the measure of angle CEB:

a) 90 degrees
b) 45 degrees
c) 60 degrees
d) 30 degrees

2. Find the measure of angles ABE, AEB, and AED:

a) Angle ABE = 45 degrees, Angle AEB = 45 degrees, Angle AED = 90 degrees
b) Angle ABE = 30 degrees, Angle AEB = 60 degrees, Angle AED = 90 degrees
c) Angle ABE = 60 degrees, Angle AEB = 30 degrees, Angle AED = 90 degrees
d) Angle ABE = 90 degrees, Angle AEB = 45 degrees, Angle AED = 30 degrees

3. Are AD and BE parallel lines?

a) Yes
b) No

Answer :

Final answer:

Angle CEB measures 90 degrees, Angle ABE measures 0 degrees, Angle AEB measures 90 degrees, Angle AED measures 90 degrees, and AD and BE are parallel lines.

Explanation:

To find the measure of angle CEB, we can use the fact that the sum of angles in a triangle is 180 degrees. Angle CEB is opposite angle AEB, so they have the same measure. Angle AEB is adjacent to angle ABE, so they add up to form a straight angle which is 180 degrees. Therefore, angle CEB has a measure of 180 - 90 = 90 degrees (Option a).

To find the measure of angle ABE, angle AEB, and angle AED, we can use the fact that opposite angles are congruent in a parallelogram. Since ABE and AED are opposite angles, they have the same measure, and they add up to form a straight angle. So, angle ABE and angle AED both have a measure of 90 degrees. Angle AEB is adjacent to both angle ABE and angle AED, so the sum of their measures is 180 degrees. Therefore, angle AEB has a measure of 180 - 90 - 90 = 0 degrees (Option b).

To determine if AD and BE are parallel lines, we can use the fact that corresponding angles formed by a transversal and two parallel lines are congruent. Angle ABE and angle AED are corresponding angles in the given diagram and they have the same measure, which is 90 degrees. Therefore, AD and BE are parallel lines (Option a).

Learn more about Angles and Parallel Lines here:

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