Grade 10 · Math · Geometry

10th grade Central angles and arc measures worksheet

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Central angles and arc measures

Grade 10 Math Worksheet

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Circle the best answer, or write your answer on the line.

Ari builds a spinner with four slices. Points C, D, F and G sit in order on circle O. What is the measure of arc DCG, in degrees?
Bo marks four points on a round clock face. Points C, D, F and G sit in order on circle O. What is the measure of arc DCG, in degrees?
Esme cuts a round pizza into four unequal slices. Points C, D, F and G sit in order on circle O. What is the measure of arc DCG, in degrees?
Jun plans four paths from the center of a round park. Points C, D, F and G sit in order on circle O. What is the measure of arc DCG, in degrees?
Kira designs a spinner with three slices. Around center O, ∠COD = (2x + 10)°, ∠DOF = (3x + 20)° and ∠FOC = 130°. What is x?
Milo plans a round rug made of three wedges. Around center O, ∠COD = (3x)°, ∠DOF = (2x + 15)° and ∠FOC = 95°. What is x?
Pia cuts a pizza in half, then cuts one half into two pieces. CD is a diameter of circle O; ∠COF = (3x + 5)° and ∠FOD = (2x + 15)°. What is x?
Ren draws a line through the center of a clock, then a hand. CD is a diameter of circle O; ∠COF = (x + 40)° and ∠FOD = (3x)°. What is x?
Tala paints a stripe across a drum top through its center, then one more. CD is a diameter of circle O; ∠COF = (4x − 10)° and ∠FOD = (x + 15)°. What is x?
Zee draws a diameter across a plate, then a radius. CD is a diameter of circle O; ∠COF = (2x + 8)° and ∠FOD = (4x − 2)°. What is x?

10th grade Central angles and arc measures worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Central angles and arc measures. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find a minor arc, a major arc or a semicircle from a central angle.
I can use the middle letter of an arc's name to tell which way round it goes.
I can solve for x when slices fill a circle or a half circle.

Standard: G-C.A.2

Words to know

central angle: An angle with its corner at the center O.

arc: A piece of the circle between two points.

minor arc / major arc: The short way round (under 180°) / the long way round (over 180°).

semicircle: Half a circle: the arc cut off by a diameter, 180°.

arc CFD: Three letters: the arc from C to D that passes through F.

whole turn: All the way round the center: 360°.

Common mistakes

Your child used 180° for a whole circle.

Your child gave the short arc when the question asked for the long way round.

Your child used 360° for half a circle.

What to say

Ask: how many degrees does a full turn on the spot take?

Ask: which way round does the middle letter of the arc's name go?

Ask: a diameter cuts the circle into two halves; how many degrees is each half?

Questions parents ask

What is the most common mistake with central angles and arc measures?

Your child used 180° for a whole circle.

How can I help my child with central angles and arc measures?

Ask: how many degrees does a full turn on the spot take?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More geometry

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