Angles formed by chords, secants and tangents

Answer Key - Grade 10 Math Worksheet

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

1. 1.

   Kira cuts two crossing lines on a round pizza. Chords CF and DG cross at H; ∠CHD = 80° and arc CD = 50°. What is the measure of arc FG?

   110
2. 2.

   Milo ices two crossing lines on a cookie. Chords CF and DG cross at H; ∠CHD = 72° and arc CD = 100°. What is the measure of arc FG?

   44
3. 3.

   Noah sews two crossing stripes on a round rug. Chords CF and DG cross at H; ∠CHD = 58° and arc CD = 76°. What is the measure of arc FG?

   40
4. 4.

   Ren draws two chain lines from Q that touch a round gear. QC and QD are tangent to circle O, and minor arc CD = 140°. What is ∠CQD, in degrees?

   40
5. 5.

   Tala walks two straight paths from Q that just touch a round pond. QC and QD are tangent to circle O, and minor arc CD = 95°. What is ∠CQD, in degrees?

   85
6. 6.

   Zee stretches two strings from Q that just touch a drum. QC and QD are tangent to circle O, and minor arc CD = 128°. What is ∠CQD, in degrees?

   52
7. 7.

   Ari looks along two paths from Q across a round pond. Secants QCD and QGF meet at Q; ∠Q = 35° and near arc CG = 40°. What is the measure of far arc DF?

   110
8. 8.

   Bo draws two lines from Q through a clock face. Secants QCD and QGF meet at Q; ∠Q = 28° and near arc CG = 50°. What is the measure of far arc DF?

   106
9. 9.

   Esme cuts two lines from Q through a round pizza. Secants QCD and QGF meet at Q; ∠Q = 42° and near arc CG = 30°. What is the measure of far arc DF?

   114
10. 10.

    Jun lays two strings from Q across a round rug. Secants QCD and QGF meet at Q; ∠Q = 50° and near arc CG = 64°. What is the measure of far arc DF?

    164