In a right-angled triangle, the sum of the two outer angles at different vertices

In a right-angled triangle, the sum of the two outer angles at different vertices is 200 degrees. Find the acute angles of this triangle.

The sum of two outer corners adjacent to sharp corners cannot be equal to 200, then this is the sum of the outer corner adjacent to a right angle and one of the acute corners.

The external angle KCB at a right angle is 90. The angle BCK = 90.

Let the angle BSC + BAM = 200, then the angle BAM = 200 – 90 = 110.

Then the adjacent angle BAC = (180 – 110) = 70.

In a right-angled triangle ABC, the angle ABC = (180 – 90 – 70) = 20.

Answer: The acute angles of the triangle are 20 and 70.