In isosceles trapezoid, obtuse angle of which is 118, inscribed in a circle.

In isosceles trapezoid, obtuse angle of which is 118, inscribed in a circle. Then the degree measure of the smaller of the arcs by which the circle is divided by the points of contact, is?

Let’s draw the radii of the circle to the points of tangency K and M. According to the properties of the tangent, the radii of the circle drawn to the point of tangency are perpendicular to the tangent itself, then the angles OKВ and OMB are straight.

Consider a BMOK quadrangle, for which the КВМ angle = 118 by condition.

Then the angle KOM = 360 – 118 – 90 – 90 = 62.

The KOM angle is the central angle of the circle, which rests on the KM arc, then the value of the degree measure of the arc is 62.

Answer: The degree measure of the smaller of the arcs is 62.