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Grade 10 · Math · Geometry

10th grade Polygons: diagonals and exterior angles worksheet

6 printable versionsBuilding Confidence10 questions · answer keyFree · no account

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Polygons: diagonals and exterior angles

Grade 10 Math Worksheet - Building Confidence

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

  1. Bo measures a rug with four right angles. Two sides are 4 ft long and the other two are 7 ft long. Which name fits the rug?

    • Convex, not regular
    • Convex and regular
    • Concave, not regular
    • Concave and regular

  2. A park map shows a five-sided flower bed that Esme will plant. Its sides have different lengths, and the angle at corner G is 200°. Which name fits the flower bed?

    • Convex, not regular
    • Convex and regular
    • Concave, not regular
    • Concave and regular

  3. Jun cuts a six-sided paper sticker with every side 4 cm. Corner F is folded in, so the angle at F is 240°. Which name fits the sticker?

    • Convex, not regular
    • Convex and regular
    • Concave, not regular
    • Concave and regular

  4. Luz draws a 9-sided rug design. A diagonal joins corner C to a corner that is not next to it. How many diagonals start at C?

  5. Milo cuts out a 14-sided paper shape. A diagonal joins corner C to a corner that is not next to it. How many diagonals start at C?

  6. Noah sketches a 16-sided window. A diagonal joins corner C to a corner that is not next to it. How many diagonals start at C?

  7. Pia walks around a five-sided park path, turning at each corner. The first four turns (exterior angles) are 72°, 85°, 64° and 58°. What is the turn at the last corner, in degrees?

  8. Ren rides a bike around a five-sided loop, turning at each corner. The first four turns (exterior angles) are 90°, 47°, 76° and 83°. What is the turn at the last corner, in degrees?

  9. Tala walks a six-sided path on a map, turning at each corner. The first five turns (exterior angles) are 50°, 62°, 48°, 71° and 59°. What is the turn at the last corner, in degrees?

  10. Zee jogs around a six-sided track, turning at each corner. The first five turns (exterior angles) are 44°, 67°, 53°, 80° and 61°. What is the turn at the last corner, in degrees?

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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

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