A straight line parallel to the base MP of an isosceles triangle MPK intersects the lateral sides at points A and B.

univerkov | December 3, 2020 | education

A straight line parallel to the base MP of an isosceles triangle MPK intersects the lateral sides at points A and B. Find the angles of triangle ABK if K = 82, M = 49 degrees.

Given:
Triangle MRK-isosceles
AB || MR
Angle M = 49 degrees
Angle K = 82 degrees
Find: angles К; КАВ and КВА
Decision:
Consider a triangle ABK-isosceles, since AK = KB
Angle KAV = Angle KVA since in an isosceles triangle the angles at the base are equal
Angle KAV = KVA = (180 degrees-angle K): 2 = (180-82): 2 = 49 degrees, since the sum of all the angles of the triangle is 180 degrees.
Answer: 82,49,49

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