In the KMNP parallelogram, the angle is M = 130 degrees, KP = 13cm. On the MN side, the point Q

univerkov | July 13, 2021 | education

In the KMNP parallelogram, the angle is M = 130 degrees, KP = 13cm. On the MN side, the point Q is marked so that MQ = 7cm, the angle KPQ = 65 degrees. Find the length of the side of the CM.

Since opposite angles in a parallelogram are equal, the angle KPN = KMN = 135.

Then the angle QPN = KPN – KPQ = 130 – 65 = 65, therefore, PQ is the bisector of the angle KPN, which means it cuts off the isosceles triangle PNQ, for which PN = QN.

In a parallelogram, the opposite sides are equal, then MN = KP = 13 cm, and QN = MN – MQ = 13 – 7 = 6 cm.

QN = PN = KM = 6 cm.

Answer: The length of the KM segment is 6 cm.

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