In parallelogram ABCD, diagonal BD is perpendicular to AB and is equal to it. Find angles.
| April 9, 2021 | education
Since, by condition, AB = BD, and AB is perpendicular to BD, then triangle ABD is rectangular and isosceles, then the angle BAD = BDA.
Angle BAD = BDA = (180 – ABD) / 2 = 90/2 = 45.
Since the opposite angles of the parallelogram are equal, and the sum of adjacent angles is 180, the angle BCD = BAD = 45, the angle ABC = ADC = 180 – BAD = 180 – 45 = 135.
Answer: The angles of the parallelogram are 45 and 135.
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