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Math: Middle School: Grades 6, 7 and 8 Quiz - Shapes - Polygons (Questions)

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A polygon is a 2-D plane (flat) shape with straight sides, such as a triangle or a pentagon. Some polygons fit together side to side as tiles to cover an area without leaving gaps. This is called tesselation.

Test your knowledge in this Math quiz.

A polygon with all sides the same length and all angles equal is called .......

[ ]	real
[ ]	reflex
[ ]	regular
[ ]	reliable

A regular quadrilateral is a .......

[ ]	rectangle
[ ]	rhombus
[ ]	square
[ ]	trapezium

The sum of the interior angles of a pentagon (5 sides) is .......

[ ]	540°
[ ]	900°
[ ]	360°
[ ]	1,080°

A polygon with n sides has an angle sum of .......

[ ]	180n
[ ]	180(n + 1)
[ ]	180(n - 1)
[ ]	180(n - 2)

The sum of the exterior angles of a polygon is .......

[ ]	180°
[ ]	360°
[ ]	720°
[ ]	it depends on the number of sides

If the exterior angle of a polygon is 45° what is the corresponding interior angle?

[ ]	75°
[ ]	108°
[ ]	135°
[ ]	160°

The exterior angle of a regular n-sided polygon is 45°. What is n?

[ ]	6
[ ]	7
[ ]	8
[ ]	9

If the interior angle of a regular n-sided polygon is 150°, what is n?

[ ]	9
[ ]	10
[ ]	11
[ ]	12

In a tile pattern of equilateral triangles, how many tiles will fit around a single point?

[ ]	3
[ ]	4
[ ]	5
[ ]	6

10.

Which of these tile shapes will not tesselate with only others of the same shape and size?

[ ]	Regular hexagon
[ ]	Isosceles triangle
[ ]	Regular octagon
[ ]	Trapezium

Math: Middle School: Grades 6, 7 and 8 Quiz - Shapes - Polygons (Answers)

A polygon with all sides the same length and all angles equal is called .......

[ ]	real
[ ]	reflex
[x]	regular
[ ]	reliable

A regular quadrilateral is a .......

[ ]	rectangle
[ ]	rhombus
[x]	square
[ ]	trapezium

The sum of the interior angles of a pentagon (5 sides) is .......

[x]	540°
[ ]	900°
[ ]	360°
[ ]	1,080°

Triangle has 180°, quadrilateral has 360°; each extra side adds 180° to total, so pentagon has 360 + 180°

A polygon with n sides has an angle sum of .......

[ ]	180n
[ ]	180(n + 1)
[ ]	180(n - 1)
[x]	180(n - 2)

3 sides 1 x 180°, 4 sides 2 x 180°, 5 sides 3 x 180°,…. n sides (n - 2) x 180°

The sum of the exterior angles of a polygon is .......

[ ]	180°
[x]	360°
[ ]	720°
[ ]	it depends on the number of sides

The exterior angle sum of any polygon, no matter how many sides, is always 360°

If the exterior angle of a polygon is 45° what is the corresponding interior angle?

[ ]	75°
[ ]	108°
[x]	135°
[ ]	160°

The sum of the exterior and interior angles at any corner is always 180° because they are angles on a straight line

The exterior angle of a regular n-sided polygon is 45°. What is n?

[ ]	6
[ ]	7
[x]	8
[ ]	9

360 ÷ 45 = 8

If the interior angle of a regular n-sided polygon is 150°, what is n?

[ ]	9
[ ]	10
[ ]	11
[x]	12

Exterior angle is 180 - 150 = 30. 360 ÷ 30 = 12

In a tile pattern of equilateral triangles, how many tiles will fit around a single point?

[ ]	3
[ ]	4
[ ]	5
[x]	6

All angles are 60° and angles around a point add up to 360°

10.

Which of these tile shapes will not tesselate with only others of the same shape and size?

[ ]	Regular hexagon
[ ]	Isosceles triangle
[x]	Regular octagon
[ ]	Trapezium

Check the angles