Question

Диагонали прямоугольника KMNP пересекаются в точке O. найдите углы треугольника KOM если угол KNP=80 градусам

Answer 1

диагонали прямоуголька равны (свойство) отсюда следует что треугольник ONP равнобедренный угол N= углу P=40 угол О=180-80=100 аналогично с треугольником окм

Answer 2

Finding the Angles of Triangle KOM

To find the angles of triangle KOM, we can use the fact that the diagonals of a rectangle bisect each other. This means that the point of intersection of the diagonals divides each diagonal into two equal parts. Given that angle KNP is 80 degrees, we can calculate the angles of triangle KOM.

1. Angle KOM: - Since the diagonals of a rectangle bisect each other, angle KOM is equal to angle KNP, which is 80 degrees.

2. Angle KMO: - Similarly, angle KMO is also equal to angle KNP, which is 80 degrees.

3. Angle OKM: - Angle OKM is the remaining angle of triangle KOM. Since the sum of the angles in a triangle is 180 degrees, we can calculate angle OKM using the formula: ``` Angle OKM = 180 - (Angle KOM + Angle KMO) ```

Therefore, ``` Angle OKM = 180 - (80 + 80) = 20 degrees ```

So, the angles of triangle KOM are: - Angle KOM = 80 degrees - Angle KMO = 80 degrees - Angle OKM = 20 degrees