The chord km is drawn in a circle with center O. Find the unknown angles of the OKM triangle if the angle KOM = 52 °

If KM is a chord, and points K and M are connected to the center O (∆KOM), then KO and MO are radii. It is impossible to draw two different radii in a circle. Therefore, KO = MO. We got a triangle in which the two sides are equal. He is isosceles. We know the angle above the base. Let’s compose and solve the equation knowing that the angles at the base are equal.
x + x + 52 ° = 180
2x = 128 °
x = 128: 2
x = 64 °
We get that the unknown angles of the triangle are 64 degrees.