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 - Challenge Me

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

Each inside angle of a regular polygon in Ari's sticker design is 135°. How many diagonals does the polygon have?
Each inside angle of a regular polygon in Esme's quilt pattern is 150°. How many diagonals does the polygon have?
Each inside angle of a regular polygon in Jun's castle tower plan is 160°. How many diagonals does the polygon have?
Read this first
Sketch, not to scale
a pentagon with each side extended and each turn labeled with its expression.
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?
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?
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?
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.
Sketch
a regular polygon split into triangles from one corner, one side extended to show the turn at a corner.
The inside angles of a regular polygon in Pia's castle floor plan add up to 1800°. What is each exterior angle, in degrees?
The inside angles of a regular polygon in Ren's park fountain plan add up to 2880°. What is each exterior angle, in degrees?
The inside angles of a regular polygon in Tala's garden bed plan add up to 720°. What is each exterior angle, in degrees?

10th grade Polygons: diagonals and exterior angles worksheet – printable — Print: 1 2 3 4 5 6

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?

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.

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