Polygons: diagonals and exterior angles

Answer Key - Grade 10 Math Worksheet - Challenge Me

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

1. 1.

   Each inside angle of a regular polygon in Ari's sticker design is 135°. How many diagonals does the polygon have?

   20
2. 2.

   Each inside angle of a regular polygon in Bo's tile pattern is 144°. How many diagonals does the polygon have?

   35
3. 3.

   Each inside angle of a regular polygon in Esme's quilt pattern is 150°. How many diagonals does the polygon have?

   54
4. 4.

   Each inside angle of a regular polygon in Jun's castle tower plan is 160°. How many diagonals does the polygon have?

   135

5. Read this first

   Sketch, not to scale

   a pentagon with each side extended and each turn labeled with its expression.

6. 5.

   Kira walks a five-sided loop in the park. The five turns (exterior angles) are (x + 6)°, (2x − 12)°, x°, (x + 24)° and (x + 18)°. What is x?

   54
7. 6.

   Luz bikes a five-sided route on a map. The five turns (exterior angles) are (2x + 9)°, (x + 10)°, (3x − 20)°, (x + 5)° and (2x + 5)°. What is x?

   39

8. Sketch

   a regular polygon split into triangles from one corner, one side extended to show the turn at a corner.

9. 7.

   The inside angles of a regular polygon in Pia's castle floor plan add up to 1800°. What is each exterior angle, in degrees?

   30
10. 8.

    The inside angles of a regular polygon in Ren's park fountain plan add up to 2880°. What is each exterior angle, in degrees?

    20
11. 9.

    The inside angles of a regular polygon in Tala's garden bed plan add up to 720°. What is each exterior angle, in degrees?

    60
12. 10.

    The inside angles of a regular polygon in Zee's picnic table plan add up to 1080°. What is each exterior angle, in degrees?

    45