In triangle ABC ∠ A = 60, 25 °, ∠B = 72, 87 ° find the value of the angle C.

Since the values ​​of the angles A and B are known, then to solve this problem we will use the theorem on the sum of the angles of a triangle – the sum of the angles of a triangle is 180º: angle A + angle B + angle C = 180º.

Let us express the value of the angle C from the theorem:

angle А + angle В + angle С = 180º – we subtract angle А from both parts.

angle A – angle A + angle B + angle C = 180º – angle A.

angle B + angle C = 180º – angle A – we subtract angle B from both parts.

angle B – angle B + angle C = 180º – angle A – angle B.

angle C = 180º – angle A – angle B.

Let us substitute the values ​​of angle A = 60.25º and angle B = 72.87º into the obtained expression: angle C = 180º – 60.25º – 72.87º = 119.75º – 72.87º = 46.88º.

Answer: Angle C is 46.88º.