Angles formed by chords, secants and tangents

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

   Kira maps two paths from Q across a round pond. Secants QCD and QGF meet at Q, outside circle O. What is ∠Q, in degrees?

   47
2. 2.

   Luz draws two lines from Q through a clock. Secants QCD and QGF meet at Q, outside circle O. What is ∠Q, in degrees?

   57
3. 3.

   Noah lays two strings from Q across a rug. Secants QCD and QGF meet at Q, outside circle O. What is ∠Q, in degrees?

   58
4. 4.

   Pia cuts two crossing lines on a round pizza. Chords CF and DG cross at H, inside circle O. What is ∠CHD, in degrees?

   95
5. 5.

   Ren draws two crossing chords on a clock face. Chords CF and DG cross at H, inside circle O. What is ∠CHD, in degrees?

   75
6. 6.

   Tala ices two crossing lines on a cookie. Chords CF and DG cross at H, inside circle O. What is ∠CHD, in degrees?

   88
7. 7.

   Zee sews two crossing stripes on a rug. Chords CF and DG cross at H, inside circle O. What is ∠CHD, in degrees?

   75
8. 8.

   Ari maps two paths from Q across a round pond. For secants QCD and QGF, ∠Q = 32°, far arc DF = (2x + 10)° and near arc CG = 46°. What is x?

   50
9. 9.

   Bo draws two lines from Q through a clock. For secants QCD and QGF, ∠Q = 43°, far arc DF = (3x − 6)° and near arc CG = 34°. What is x?

   42
10. 10.

    Jun lays two strings from Q across a rug. For secants QCD and QGF, ∠Q = 52°, far arc DF = (5x + 4)° and near arc CG = 60°. What is x?

    32