Inscribed angles and inscribed quadrilaterals

Answer Key - Grade 10 Math Worksheet

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

1. 1.

   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?

   74
2. 2.

   Esme looks across a round pizza from its crust. Points C, D and F lie on circle O, and ∠CDF = 66°. What is the measure of arc CF?

   132
3. 3.

   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?

   96
4. 4.

   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?

   162
5. 5.

   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?

   30
6. 6.

   Milo joins four points on a clock face. Quadrilateral CDFG is inscribed in circle O, with ∠C = (4x − 6)° and ∠F = (x + 21)°. What is x?

   33
7. 7.

   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?

   25
8. 8.

   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?

   10
9. 9.

   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?

   8
10. 10.

    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?

    7