Skills · Geometry · Circles

Inscribed angles

Printable practice with an answer key the engine computes, at three levels, in as many versions as you need.

Problem types

Sample Sheet · Level 1

  1. circle with inscribed angle ABC: ∠ABC 60°, arc AC ?ABC60°?
    Find the measure marked ?.
  2. circle with inscribed angle ABC: ∠ABC ?, arc AC 200°ABC?200°
    Find the measure marked ?.
  3. circle with inscribed angle ABC: ∠ABC ?, arc AC 56°ABC?56°
    Find the measure marked ?.
  4. circle O, diameter AC, B on the circle: ∠BAC ?, ∠BCA 60°OABC?60°
    AC is a diameter. Find the measure marked ?.
  5. circle O, diameter AC, B on the circle: ∠BAC 37°, ∠BCA ?OABC37°?
    AC is a diameter. Find the measure marked ?.
  6. circle O, diameter AC, B on the circle: ∠BAC 35°, ∠BCA ?OABC35°?
    AC is a diameter. Find the measure marked ?.
  7. circle with inscribed angle ABC: ∠ABC 78°, arc AC ?ABC78°?
    Find the measure marked ?.
  8. circle with inscribed angle ABC: ∠ABC ?, arc AC 120°ABC?120°
    Find the measure marked ?.

Answer key

  1. 120°
  2. 100°
  3. 28°
  4. 30°
  5. 53°
  6. 55°
  7. 156°
  8. 60°

Sample Sheet · Level 3

  1. circle O, diameter AC, B on the circle: ∠BAC (x + 9)°, ∠BCA (x + 21)°OABC(x + 9)°(x + 21)°
    AC is a diameter. Find m∠BAC.
  2. circle with inscribed angle ABC: ∠ABC (2x − 36)°, arc AC (x + 15)°ABC(2x − 36)°(x + 15)°
    Find m⌒AC.
  3. circle with inscribed angle ABC: ∠ABC (3x − 14)°, arc AC (2x + 32)°ABC(3x − 14)°(2x + 32)°
    Find m∠ABC.
  4. quadrilateral ABCD inscribed in a circle: ∠B (x + 45)°, ∠D (3x + 27)°ABCD(x + 45)°(3x + 27)°
    ABCD is inscribed in the circle. Find m∠B.
  5. circle with inscribed angle ABC: ∠ABC (x + 46)°, arc AC (7x − 38)°ABC(x + 46)°(7x − 38)°
    Find m⌒AC.
  6. quadrilateral ABCD inscribed in a circle: ∠A (4x − 40)°, ∠C (3x + 17)°ABCD(4x − 40)°(3x + 17)°
    ABCD is inscribed in the circle. Find m∠A.
  7. circle O, diameter AC, B on the circle: ∠BAC (4x − 7)°, ∠BCA (5x − 47)°OABC(4x − 7)°(5x − 47)°
    AC is a diameter. Find m∠BAC.
  8. circle with inscribed angle ABC: ∠ABC (x + 35)°, arc AC (8x − 50)°ABC(x + 35)°(8x − 50)°
    Find m∠ABC.

Answer key

  1. 39°
  2. 44°
  3. 31°
  4. 72°
  5. 144°
  6. 76°
  7. 57°
  8. 55°

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