Diagonal BD of parallelogram ABCD makes angles of 45 and 75 degrees with its sides. Find the acute angle of parallelogram.
| February 24, 2021 | education
Determine the value of the angle ABC.
Angle ABC = AВD + СВD = 75 + 45 = 120.
A parallelogram has a sum of adjacent angles equal to 180.
Then the angle ВAD = (180 – ABC) = (180 – 120) = 60.
In a parallelogram, the opposite angles are equal, then the angle of ВСD = ВAD = 600, angle ADС = ABC = 120.
Answer: The acute angle of the parallelogram is 60.
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