A parallelogram is a quadrilateral in which opposite sides are pairwise parallel and equal.
The opposite angles of the parallelogram are also equal to each other:
∠А = ∠С;
∠В = ∠Д.
Since the sum of the degree measures of the angles adjacent to one side of the parallelogram is 180º, and the value of the angle ∠A is equal to the value of two angles ∠B, we will express it as follows:
x is the degree measure of the angle ∠В;
2x – degree measure of angle ∠A;
x + 2x = 180;
3x = 180;
x = 180/3 = 60;
∠В = 60º;
∠А = 60º · 2 = 120º.
Answer: the angle a ∠A is equal to 120º, ∠B is equal to 60º.
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