In parallelogram ABCD, the height BH is half the side of CD. Find the degree measure of the angle ABC.
| January 17, 2021 | education
Since the opposite sides of the parallelogram are equal, then AB = СD.
By condition, ВН = СD / 2, then in a right-angled triangle AВН, ВН = AB / 2.
Then SinВAD = ВН / AB = (AB / 2) / AB = 1/2.
Angle ВAD = arcsin (1/2) = 30.
In a parallelogram, the sum of adjacent angles is 180, then the angle ABC = 180 – ВAD = 180 – 30 = 150.
Answer: Angle ABC is 150.
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