In parallelogram ABCD, point K is marked on the BC side so that BK = AB. Find the angle ВСD, if the angle КAD = 20 °.
| February 10, 2021 | education
Since, by condition, AB = ВK, then the triangle AВK is isosceles, which means the angle ВAK = ВKA.
Angle KAD = ВKA as criss-crossing angles when crossing parallel straight lines ВС and АС secant to AK. Then the angle ВAK = ВKA = KAD = 20.
Determine the value of the angle ABC.
Angle ABC = 180 – 20 – 20 = 140, then angle ABC = 180 – 140 = 40.
Since the opposite angles of the parallelogram are equal, the ВСD angle = VAD = 40.
Answer: The ВСD angle is 40.
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