The angle M of the triangle MHK is 2 times less than the angle H and 3 times less than the angle K.

The angle M of the triangle MHK is 2 times less than the angle H and 3 times less than the angle K. Find all the corners of the triangle.

According to the conditions, the angle M is 2 times less than the angle H and 3 times less than the angle K, therefore, the angle H = 2M, the angle K = 3M.

Let’s compose an expression:

MНK = M + H + K = M + 2M + 3M.

By the theorem on the sum of the angles of a triangle, the sum of the angles is 180. We get:

M + 2M + 3M = 180.

We got an equation where M is a variable. Therefore, we can apply the rule of addition of similar terms (terms that have the same letter part):

M (1 + 2 + 3) = 180

6M = 180

M = 30.

Find the remaining angles of the MНК triangle:

H = 2M = 2 * 30 = 60.

K = 3M = 3 * 30 = 90.