In an isosceles triangle MNK with a base MK, the bisector KE of the outer angle NKF makes an angle of 30 °

In an isosceles triangle MNK with a base MK, the bisector KE of the outer angle NKF makes an angle of 30 ° with the ray KP, perpendicular to MF. Find the degree measure of the angle MNK.

Since KP is perpendicular to MF, then the angle of PKF is straight, then the angle EKF = 90 – 30 = 60.

Since KE is the bisector of the angle NKF, then the angle NKF = 60 * 2 = 120.

Internal angle MKN adjacent to angle NKF, then angle MKN = 180 – 120 = 60.

Then the isosceles triangle MNK is equilateral, and therefore the angle is MNK = 60.

Answer: Angle MNK = 60.