In the parallelogram ABCD on the side BC, point E is marked so that AB = BE. Find the angle BCD if the angle EAD = 30 degrees.
Angle BEA = angle EAD = 30 ° (internal cross lying).
Consider a triangle ABE, it is isosceles (AB = BE according to the problem statement), which means that the angles at the base are equal: angle BEA = angle BAE = 30 °. Find the degree measure of the vertex of an isosceles triangle, that is, the angle ABE:
Angle ABE = 180 ° – (30 ° + 30 °) = 180 ° – 60 ° = 120 °
Find the corner BCD, it is adjacent (adjacent) to the angle ABE. The sum of adjacent (adjacent) angles in a parallelogram is 180 °.
angle BCD = 180 ° – angle ABE = 180 ° – 120 ° = 60 °
Answer: The BCD angle is 60 °.
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