1. x = 70° (Opposite angles in a cyclic quadrilateral are supplementary)
2. x = 85°, y = 54° (Angles in alternate segments are equal to the angle between the tangent and chord)
3. x = 60° (Angle at the center is twice the angle at the circumference subtended by the same arc; 120° / 2 = 60°)
4. x = 80° (Angle at the center is twice the angle at the circumference subtended by the same arc; 40° * 2 = 80°)
5. x = 150° (Angle at the center is twice the angle at the circumference subtended by the same arc; 75° * 2 = 150°)
6. x = 40° (Angle at the center is twice the angle at the circumference subtended by the same arc; 20° * 2 = 40°)
7. x = 60° (Angles in the same segment are equal; the triangle formed is isosceles with base angles equal, and angles in the same segment are equal)
8. x = 50° (Angle at the circumference is half the angle at the center subtended by the same arc; 100° / 2 = 50°)
Parent Tip: Review the logic above to help your child master the concept of geometric circles worksheet.