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.

   Luz draws every diagonal from one corner of an 11-sided shape drawn in pencil. How many triangles does that make?

   9
5. 5.

   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
6. 6.

   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
7. 7.

   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
8. 8.

   Diagonals from one corner split a seven-sided shape cut from paper into 5 triangles, as Ren's sketch shows. What do all its inside angles add up to, in degrees?

   900
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