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

NameDate

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

Bo stands on the edge of a round pond. Points C, D and F lie on circle O, and ∠CDF = 37°. What is the measure of arc CF?
Jun draws two lines from a point on a clock's rim. Points C, D and F lie on circle O, and ∠CDF = 48°. What is the measure of arc CF?
Kira draws two lines from a point on a drum's rim. Points C, D and F lie on circle O, and ∠CDF = 81°. What is the measure of arc CF?
Luz builds a window frame inside a round opening. Quadrilateral CDFG is inscribed in circle O, with ∠C = (2x + 10)° and ∠F = (3x + 20)°. What is x?
Noah ices a four-sided shape on a round cookie. Quadrilateral CDFG is inscribed in circle O, with ∠C = (3x + 4)° and ∠F = (2x + 16)°. What is x?
Pia sews a four-sided patch on a round rug. Quadrilateral CDFG is inscribed in circle O, with ∠C = (5x)° and ∠F = (x + 30)°. What is x?
Ren looks across a round pond from two spots on its edge. On circle O, ∠CDF = (3x + 5)° and ∠CGF = (x + 25)°; both open onto arc CF. What is x?
Tala looks at the same crust from two spots on a round pizza. On circle O, ∠CDF = (4x − 8)° and ∠CGF = (2x + 14)°; both open onto arc CF. What is x?
Zee draws two angles on a clock face. On circle O, ∠CDF = (5x + 2)° and ∠CGF = (3x + 18)°; both open onto arc CF. What is x?
Ari paints two angles on a drum top. On circle O, ∠CDF = (6x − 5)° and ∠CGF = (4x + 9)°; both open onto arc CF. What is x?

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

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

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.

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.

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?

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.

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