In a right-angled triangle KLM, the angle M is 90 degrees, the bisectors ME and KF

In a right-angled triangle KLM, the angle M is 90 degrees, the bisectors ME and KF meet at point O. The angle KOM is 100 degrees. Find all the acute corners of the triangle KLM.

Since ME is the bisector of a right angle, the angle LME = EMK = 90/2 = 45.

In the triangle MОК, we define the value of the angle OKM.

Angle PKM = 180 – MOK – OMK = 180 – 100 – 45 = 35.

Since KF is the bisector of the MKL angle, the MKL angle = 35 * 2 = 70.

Then the angle MLK = 180 – 90 – MKL = 180 – 90 – 70 = 20.

Answer: The angles of the triangle KLM are 90, 70, 20.