Apply circle theorems

O is the centre of the circle. Find x, giving reasons:

1. Angle at centre = 100°, angle at circumference on same arc = x.
2. Angle in a semicircle subtended by diameter, x.
3. Cyclic quadrilateral with angles 85°, x, 70°, y. Find x.
4. Two angles in the same segment: 40° and x.
5. Tangent meets radius. Angle between tangent and radius = x.

Submit Exercise