In the isosceles triangle MNP, the bisector NK is drawn to the base of the MP, the angle MNK = 32 degrees, MP = 20 cm

In the isosceles triangle MNP, the bisector NK is drawn to the base of the MP, the angle MNK = 32 degrees, MP = 20 cm, Find the angle N, the angle NKP, KP, the value of the outer angle at the vertex P.

1. Based on the fact that the bisector drawn from the top of an isosceles triangle is the median and height, that is, it forms a right angle with the base and divides the base into two equal parts, and the warping angles are equal, we calculate:

Angle NKP = 90 °.

KR = MR / 2 = 20: 2 = 10 cm.

Angle МNР = 32 ° + 32 ° = 64 °.

2. Angle NMP = angle MPN = (180 ° – 64 °) / 2 = 58 °.

3. Outside angle at the apex P = 180 ° – 58 ° = 122 °.

Answer: КР = 10 cm, angle NКР = 90 °, external angle at the apex Р = 122 °, angle МNР = 64 °.