# In the isosceles triangle KLT, the bisector TM of the angle T is drawn at the base of the KT, ∡TML = 96 °.

**In the isosceles triangle KLT, the bisector TM of the angle T is drawn at the base of the KT, ∡TML = 96 °. Determine the angles of this triangle.**

The TM bisector divides the angle in half.

The corners TML and TMC are adjacent.

The sum of adjacent angles is 180 degrees.

Since the TML angle is 96 degrees.

So the angle of TMK is equal to:

180 gr -96 gr = 84 gr.

Further:

Let’s take the angle MTC as x.

This means that the angle of TCL is 2x.

Let’s make the equation:

x + 2x + 84 = 180 gr.

3x = 180-84.

3x = 96.

x = 96/3.

x = 32.

Further:

we find the angle of TCM.

32×2 = 64gr.

Since in an isosceles triangle the angles at the base are equal, then

MKT angle = LTK angle = 64 degrees.

Find the KLT angle.

180gr- (64 + 64) = 52gr.

Answer: angle K = angle T = 64 degrees, angle A = 52 degrees.