The heights of the triangle ABC, drawn from the vertices A and C intersect at point M.

The heights of the triangle ABC, drawn from the vertices A and C intersect at point M. Find the angle AMC, if the angle A = 70 угол, angle C = 80˚

Determine the value of the angle ABC, knowing that the sum of the inner angles of the triangle is 180.

Then the angle ABC = (180 – BAC – AСB) = (180 – 70 – 80) = 30.

EC and AH are the heights of triangle ABC, then the angle BEC and BHA are equal to 90.

The sum of the angles of the quadrilateral ВEMН is 3600, then the angle EON = (360 – ВEM – ВНM – EBН) = (360 – 90 – 90 – 30) = 150. Angle AMC = EMH as vertical angles at the intersection of the heights AH and CE, then the angle AOC = 150.

Answer: The angle of the AMC is 150.