Inscribed angles and inscribed quadrilaterals

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

   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?

   70
2. 2.

   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?

   115
3. 3.

   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?

   80
4. 4.

   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?

   95
5. 5.

   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?

   85
6. 6.

   Noah joins four points on a big clock face. Quadrilateral CDFG is inscribed in circle O, with arcs CD = 95°, DF = 75° and FG = 125°. What is ∠C, in degrees?

   100
7. 7.

   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?

   56
8. 8.

   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?

   47
9. 9.

   Zee draws a triangle on a clock face. CF is a diameter of circle O, D is on the circle, ∠DCF = (x + 12)° and ∠DFC = (4x − 2)°. What is ∠DCF?

   28
10. 10.

    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?

    68