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Grade 10 · Math · Geometry

10th grade Polygons: diagonals and exterior angles worksheet

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Polygons: diagonals and exterior angles

Grade 10 Math Worksheet

NameDate

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

  1. Esme draws every diagonal of a 13-sided star sticker outline. How many diagonals are there in all?

  2. Jun draws every diagonal of a 15-sided table top plan. How many diagonals are there in all?

  3. Kira draws every diagonal of a 20-sided sun design. How many diagonals are there in all?

  4. Luz draws every diagonal of a 10-sided paper badge. How many diagonals are there in all?

  5. Milo walks around a path shaped like a regular 15-sided polygon, turning the same amount at each corner. What is each exterior angle (turn), in degrees?

  6. Noah walks around a regular 24-sided garden path, turning the same amount at each corner. What is each exterior angle (turn), in degrees?

  7. Pia rides around a regular 40-sided track, turning the same amount at each corner. What is each exterior angle (turn), in degrees?

  8. Each exterior angle (turn) of a regular polygon in Ren's honeycomb tile design is 60°. How many sides does the polygon have?

  9. Each exterior angle (turn) of a regular polygon in Tala's floor tile design is 90°. How many sides does the polygon have?

  10. Each exterior angle (turn) of a regular polygon in Zee's sticker design is 120°. How many sides does the polygon have?

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10th grade Polygons: diagonals and exterior angles worksheet – printable
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About this worksheet

Polygons: diagonals and exterior angles. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can tell whether a polygon is convex or concave, and whether it is regular.
  • I can count the diagonals of a polygon, from one corner and in all.
  • I can use "the turns add to 360°" to find an exterior angle or the number of sides.

Standard: no CCSS high school standard (G-CO.A.1 related)

Words to know

diagonal: A segment joining two corners that are not next to each other.

exterior angle (turn): The turn you make at a corner when walking around the shape.

inside angle: The angle inside the shape at a corner; it and the turn add to 180°.

convex / concave: Every angle under 180° / one angle over 180°, a dent.

regular: All sides equal and all angles equal.

Common mistakes

Your child called a polygon regular after checking only its sides or only its angles. Regular needs both: all sides equal and all angles equal. Look at a rectangle together: equal angles, but not regular.

Your child missed an angle over 180°, which makes a polygon concave (it has a dent).

Your child counted the triangles the diagonals make, not the diagonals. There is one fewer diagonal than triangles. Draw a hexagon and count both.

What to say

Ask: does any corner point in toward the middle?

Questions parents ask

What is the most common mistake with polygons: diagonals and exterior angles?

Your child called a polygon regular after checking only its sides or only its angles. Regular needs both: all sides equal and all angles equal. Look at a rectangle together: equal angles, but not regular.

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More geometry

See all Geometry

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