A closed two-dimensional figure formed by three or more straight line segments connected end-to-end.
Connect-the-dots that closes into a shape—no curves allowed.
Showing a random 20 of 50 problems.
Example 1
medium
What is the sum of the exterior angles of any polygon, one at each vertex?
Example 2
easy
What is the sum of the exterior angles of any convex polygon?
Example 3
hard
A polygon has interior-angle sum equal to four times its exterior-angle sum. Find the number of sides.
Example 4
easy
How many sides does a polygon with interior-angle sum 1080∘ have?Octagon: interior angle sum = 1080°
Example 5
easy
Each interior angle of a regular polygon is 108∘. How many sides does it have?Regular pentagon — each interior angle = 108°
Example 6
medium
A regular polygon's interior angle is three times its exterior angle. Find the number of sides.Regular octagon: interior 135° = 3 × exterior 45°, so n = 8
Example 7
hard
A regular polygon has each interior angle measuring 172∘. How many sides does it have?
Example 8
medium
The interior angles of a quadrilateral are in the ratio 1:2:3:4. Find each angle.
Example 9
easy
Is a shape with one curved side and two straight sides a polygon?
Example 10
hard
For how many values of n≥3 is the interior angle of a regular n-gon a whole number of degrees?
Example 11
challenge
In a convex polygon, all but one of the interior angles each measure 150∘, and the remaining interior angle measures 90∘. How many sides does the polygon have?
Example 12
easy
What is a 7-sided polygon called?
Example 13
hard
How many distinct triangles can be formed by choosing 3 vertices from a convex octagon?
Example 14
easy
Find the sum of the interior angles of a pentagon (5 sides).Pentagon: (5 − 2) × 180° = 540°
Example 15
medium
How many diagonals does a pentagon have?
Example 16
medium
Find the sum of the interior angles of a hexagon (6 sides).Hexagon interior angle sum: 6 × 120° = 720°
Example 17
medium
A regular hexagon has perimeter 48 cm. Find each side length.Regular hexagon: 6 × 8 cm = 48 cm perimeter
Example 18
challenge
A convex polygon has 35 diagonals. How many sides does it have?
Example 19
hard
A polygon has an interior angle sum of 1980°. How many sides does it have?
Example 20
medium
A polygon has 44 diagonals. How many sides does it have?