The ABC triangle is inscribed in a circle centered at the point O.

The ABC triangle is inscribed in a circle centered at the point O. Find the degree measure of the angle C of the ABC triangle if the ABO angle is 23 degrees.

Consider an isosceles triangle AOB (OA = OB – the radii of the circumscribed circle). ABO angle – angle at the base of an isosceles triangle. We find the angle at the vertex, it is also the central angle AOB, which rests on the arc AB:
∠ AOB = 180 ° – (23 ° + 23 °) = 134 °.
The inscribed angle ACB rests on the same arc AB. Its degree measure is equal to half the degree measure of the central angle:
∠ АСВ = ∠ AOB / 2 = 134/2 = 67 °.
Answer: the angle C of the triangle ABC is 67 °.