Inscribed angles and inscribed quadrilaterals

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

1. 1.

   Bo stands at the edge of a round pizza table. Points C, D and F lie on circle O, and arc CF = 84°. What is ∠CDF, in degrees?

   42
2. 2.

   Esme stands on the edge of a round pond and looks across. Points C, D and F lie on circle O, and arc CF = 136°. What is ∠CDF, in degrees?

   68
3. 3.

   Kira places three candles on the edge of a round cake. Points C, D and F lie on circle O, and arc CF = 150°. What is ∠CDF, in degrees?

   75
4. 4.

   Luz cuts a pizza straight through the middle, then cuts to the crust. CF is a diameter of circle O, D is on the circle, and ∠DCF = 36°. What is ∠DFC, in degrees?

   54
5. 5.

   Milo draws a triangle on a plate with one side across the middle. CF is a diameter of circle O, D is on the circle, and ∠DCF = 63°. What is ∠DFC, in degrees?

   27
6. 6.

   Noah draws a triangle on a clock face with one side through the center. CF is a diameter of circle O, D is on the circle, and ∠DCF = 25°. What is ∠DFC, in degrees?

   65
7. 7.

   Pia paints a triangle on a drum top with one side through the center. CF is a diameter of circle O, D is on the circle, and ∠DCF = 47°. What is ∠DFC, in degrees?

   43
8. 8.

   Tala joins four points on a clock face. Quadrilateral CDFG is inscribed in circle O, and ∠C = 119°. What is ∠F, in degrees?

   61
9. 9.

   Zee pipes a four-sided shape with corners on a cookie's edge. Quadrilateral CDFG is inscribed in circle O, and ∠C = 98°. What is ∠F, in degrees?

   82
10. 10.

    Ari sews a four-sided patch with its corners on a round rug's edge. Quadrilateral CDFG is inscribed in circle O, and ∠C = 61°. What is ∠F, in degrees?

    119