Find the measure of angle O.

Based on the image, we have a circle with an inscribed triangle. Two sides of the triangle are marked as equal, which means it's an isosceles triangle. The angle opposite the base is labeled as 62 degrees. We want to find the measure of angle O, which I assume refers to the angle at the center of the circle subtended by the base of the isosceles triangle. First, let's find the measures of the base angles of the isosceles triangle. Let each of these angles be $$x$$. Since the sum of the angles in a triangle is 180 degrees, we have: $$x + x + 62 = 180$$ $$2x = 180 - 62$$ $$2x = 118$$ $$x = 59$$ So each of the base angles is 59 degrees. Now, let's consider the angle at the center, angle O. The inscribed angle (59 degrees) subtends the same arc as the central angle O. The central angle is twice the inscribed angle subtending the same arc. $$O = 2 * 59$$ $$O = 118$$ Answer: The measure of angle O is 118 degrees.