Start free
Back to the topic
Free printable worksheetlessoons.com

Euclidean Geometry: Triangles and Circles · Ages 15–16

Central and Inscribed Angles Practice

Name: Date:

This worksheet is for 10th-grade geometry students. Use the relationship between central angles, inscribed angles, and intercepted arcs to solve each question.

  1. Arc AB measures 84 degrees. Central angle AOB intercepts arc AB. What is the measure of angle AOB?

  2. Inscribed angle APB intercepts arc AB, which measures 84 degrees. What is the measure of angle APB?

  3. In circle O, central angle COD measures 130 degrees. Inscribed angle CED intercepts the same arc CD. Find the measure of angle CED.

  4. Segment XY is a diameter of circle O. Point Z is a point on the circle distinct from X and Y. What is the measure of angle XZY?

  5. Two inscribed angles, angle PRQ and angle PSQ, intercept the exact same arc PQ. If angle PRQ measures 38 degrees, what is the measure of angle PSQ?

  6. In circle O, chord AB is congruent to chord CD. Central angle AOB measures 54 degrees. Inscribed angle CPD intercepts arc CD. What is the measure of angle CPD?

More topics and worksheets at lessoons.com© 2026 Lessons · 1 / 2
Answer keylessoons.com

Central and Inscribed Angles Practice

Answer key

  1. Arc AB measures 84 degrees. Central angle AOB intercepts arc AB. What is the measure of angle AOB?

    84 degrees. The central angle equals the measure of its intercepted arc.

  2. Inscribed angle APB intercepts arc AB, which measures 84 degrees. What is the measure of angle APB?

    42 degrees. An inscribed angle is half the measure of its intercepted arc (84 / 2 = 42).

  3. In circle O, central angle COD measures 130 degrees. Inscribed angle CED intercepts the same arc CD. Find the measure of angle CED.

    65 degrees. An inscribed angle is half of the central angle on the same arc (130 / 2 = 65).

  4. Segment XY is a diameter of circle O. Point Z is a point on the circle distinct from X and Y. What is the measure of angle XZY?

    90 degrees. An angle inscribed in a semicircle is always a right angle.

  5. Two inscribed angles, angle PRQ and angle PSQ, intercept the exact same arc PQ. If angle PRQ measures 38 degrees, what is the measure of angle PSQ?

    38 degrees. Inscribed angles that intercept the same arc are equal.

  6. In circle O, chord AB is congruent to chord CD. Central angle AOB measures 54 degrees. Inscribed angle CPD intercepts arc CD. What is the measure of angle CPD?

    27 degrees. Congruent chords subtend congruent arcs, so central angle COD also measures 54 degrees. Inscribed angle CPD is half of that measure (54 / 2 = 27).