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 Bo's tile pattern is 144°. How many diagonals does the polygon have?

   35
2. 2.

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

   54
3. 3.

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

   135

4. Read this first

   Sketch, not to scale

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

5. 4.

   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
6. 5.

   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. 6.

   Milo rides a scooter around a six-sided rink. The six turns (exterior angles) are x°, (x + 10)°, (x − 5)°, (x + 15)°, (x + 20)° and (x − 4)°. What is x?

   54
9. 7.

   Noah walks a six-sided path around a pond. The six turns (exterior angles) are 2x°, (x + 12)°, (2x − 6)°, (x + 10)°, (3x − 14)° and (x + 18)°. What is x?

   Use the picture in question 6.

   34

10. Sketch

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

11. 8.

    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
12. 9.

    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
13. 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