In a circle whose center is O, arc AB contains 100°. Find the number of degrees in angle ABO.
To find the number of degrees in angle ABO, we need to use the central angle theorem. According to the theorem, the central angle is equal to the measure of its intercepted arc. In other words, angle ABO is equal to arc AB.
Given that arc AB contains 100°, we can conclude that the measure of angle ABO is also 100°. So the number of degrees in angle ABO is 100°.
ABO is an isosceles triangle ... AO and BO are radii of the circle
... so angles A and B are equal ... A = B
central angle O equals the arc AB ... O = 100º
A + B + O = 180º