On one side of the straight line AC, points B and K are marked so that AB = CK, AK = CB, angle BAC = 82

| April 9, 2021 | education

On one side of the straight line AC, points B and K are marked so that AB = CK, AK = CB, angle BAC = 82 degrees, angle BCA = 39 degrees. What is the BAK angle?

Based on the conditions of this problem, connecting in pairs the points A and B, B and C, K and C, K and A, we have two acute-angled triangles.

Triangles ABC and КAС are equal according to the third sign of equality of triangles: if three sides of one triangle are equal, respectively, to three sides of the second triangle, then such triangles are equal.

They have a side AB = KС, according to the condition of the problem, side BC = AK according to the condition of the problem, and the third side of the AC is common.

If the triangles are equal, then the corresponding angles are equal.

Hence the angle KAС = BCA = 39 degrees. We have an angle BAC = BAC – КAС = 82 – 39 = 43 (degrees).

Answer: angle BAC = 43 degrees.



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