Angles of a polygon: add up the triangles

Answer Key - Grade 8 Math Worksheet - Building Confidence

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

1. 1.

   Esme draws every diagonal from one corner of a 5-sided paper shape. How many triangles does that make?

   3
2. 2.

   Jun draws every diagonal from one corner of a 13-sided paper cut-out. How many triangles does that make?

   11
3. 3.

   Kira draws every diagonal from one corner of a 15-sided paper cut-out. How many triangles does that make?

   13
4. 4.

   Diagonals from one corner split a paper pentagon into 3 triangles, as Milo's sketch shows. What do all its inside angles add up to, in degrees?

   540
5. 5.

   Diagonals from one corner split a hexagon paper cut-out into 4 triangles, as Noah's sketch shows. What do all its inside angles add up to, in degrees?

   720
6. 6.

   Diagonals from one corner split an octagon shape drawn on paper into 6 triangles, as Pia's sketch shows. What do all its inside angles add up to, in degrees?

   1080
7. 7.

   a pentagon split into 3 triangles, with 540° written inside; angles 100°, 110°, 95°, 120° and x°. Tala's paper pentagon has four angles of 100°, 110°, 95° and 120°. The sketch writes 540° inside it. What is the fifth angle, in degrees?

   115
8. 8.

   “Sketch, not to scale:” Zee's pentagon paper cut-out has four angles of 130°, 85°, 105° and 98°. The sketch writes 540° inside it. What is the fifth angle, in degrees?

   122
9. 9.

   Ari's pentagon shape cut from paper has four angles of 92°, 118°, 104° and 126°. The sketch writes 540° inside it. What is the fifth angle, in degrees?

   100
10. 10.

    Bo's pentagon shape drawn on paper has four angles of 140°, 76°, 112° and 101°. The sketch writes 540° inside it. What is the fifth angle, in degrees?

    111