The segments AE and DC intersect at point B, which is the midpoint of each of them. 1) Prove that triangle

The segments AE and DC intersect at point B, which is the midpoint of each of them. 1) Prove that triangle ABC = triangle EBD. 2) Find the angle A and angle C of triangle ABC, if the triangle in the triangle is angle D = 47 degrees, angle E = 42 degrees

1) Given:
segments AE and DC intersect at point B,
AB = BE,
CE = ED.
Prove that triangle ABC = triangle EBD.
Evidence:
Triangle ABC = triangle EBD on two sides and the angle between them, since AB = BE, CE = ED and angle AOC = angle DBE – they are vertical. Q.E.D;
2) Given:
segments AE and DC intersect at point B,
AB = BE,
CE = ED,
angle D = 47 degrees,
angle E = 42 degrees.
Find the degree measure of angle A and angle B.
Decision:
Since triangle ABC = triangle EBD, then angle A = angle D = 47 degrees, angle E = angle C = 42 degrees.
Answer: 47 degrees; 42 degrees.