Grade 10 · Math · Geometry

10th grade Inscribed angles and inscribed quadrilaterals worksheet

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Inscribed angles and inscribed quadrilaterals

Grade 10 Math Worksheet - Challenge Me

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

Bo cuts a triangle out of a round pizza, corners on the crust. △CDF is inscribed in circle O, with arc CD = 100° and arc DF = 120°. What is ∠CDF, in degrees?
Esme paints a triangle on a round plate, corners on the rim. △CDF is inscribed in circle O, with arc CD = 60° and arc DF = 70°. What is ∠CDF, in degrees?
Jun ices a triangle on a round cookie, corners on the edge. △CDF is inscribed in circle O, with arc CD = 50° and arc DF = 90°. What is ∠CDF, in degrees?
Kira joins three points on a clock face. △CDF is inscribed in circle O, with arc CD = 110° and arc DF = 90°. What is ∠CDF, in degrees?
Luz designs a four-sided window in a round frame. Quadrilateral CDFG is inscribed in circle O, with arcs CD = 80°, DF = 90° and FG = 100°. What is ∠C, in degrees?
Milo sews a four-sided patch on a round rug. Quadrilateral CDFG is inscribed in circle O, with arcs CD = 70°, DF = 110° and FG = 60°. What is ∠C, in degrees?
Pia ices a four-sided shape on a round cookie. Quadrilateral CDFG is inscribed in circle O, with arcs CD = 60°, DF = 130° and FG = 84°. What is ∠C, in degrees?
Ren cuts a pizza through the middle. CF is a diameter of circle O, D is on the circle, ∠DCF = (2x + 6)° and ∠DFC = (x + 9)°. What is ∠DCF?
Tala draws a triangle on a plate. CF is a diameter of circle O, D is on the circle, ∠DCF = (3x − 4)° and ∠DFC = (2x + 9)°. What is ∠DCF?
Ari paints a triangle on a drum top. CF is a diameter of circle O, D is on the circle, ∠DCF = (5x + 3)° and ∠DFC = (x + 9)°. What is ∠DCF?

10th grade Inscribed angles and inscribed quadrilaterals worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Inscribed angles and inscribed quadrilaterals. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can find an inscribed angle from its arc, and the arc from the angle.
I can use the right angle in a semicircle.
I can use opposite angles of a quadrilateral in a circle adding to 180°.

Standard: G-C.A.2, G-C.A.3

Words to know

inscribed angle: An angle with its corner on the circle and its sides as chords.

intercepted arc: The arc that lies between the angle's two sides.

inscribed quadrilateral: A four-sided shape with all four corners on the circle.

opposite angles: Two corners of a quadrilateral that are not next to each other.

diameter: A chord through the center; it cuts the circle into two 180° halves.

Common mistakes

Your child treated an angle on the circle like an angle at the center.

Your child doubled the arc instead of halving it.

Your child forgot that an angle in a semicircle is a right angle.

What to say

Ask: is the corner of this angle at the center or on the circle?

Ask: is an angle on the circle bigger or smaller than its arc?

Ask: CF is a diameter; what is the angle at D?

Questions parents ask

What is the most common mistake with inscribed angles and inscribed quadrilaterals?

Your child treated an angle on the circle like an angle at the center.

How can I help my child with inscribed angles and inscribed quadrilaterals?

Ask: is the corner of this angle at the center or on the circle?

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

See all Geometry

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