Regular Polygons: Angles, Diagonals & Formulas

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| Questions: 20 | Updated: Nov 21, 2025
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1) The sum of interior angles of a regular hexagon is:

Explanation

Sum of interior angles = ( n − 2 ) × 180 = ( 6 − 2 ) × 180 = 720°.

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About This Quiz
Regular Polygons: Angles, Diagonals & Formulas - Quiz

Get ready to discover the hidden math inside regular polygons! In this quiz, you’ll calculate interior and exterior angles, find the sum of angles, and work out how many diagonals a polygon has. You’ll also see how special formulas help with hexagons, octagons, and more. With each problem, you’ll grow... see moremore confident in measuring and describing these shapes.
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2) The measure of each exterior angle of a regular octagon is:

Explanation

The exterior angle of a regular polygon can be calculated using the formula 360° divided by the number of sides. For an octagon, which has 8 sides, each exterior angle is 360°/8 = 45°.

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3) The formula for the sum of interior angles of an n-sided polygon is:

Explanation

The sum of the interior angles of an n-sided polygon is calculated using the formula 180(n–2) degrees. This formula derives from the fact that a polygon can be divided into (n–2) triangles, and since each triangle has interior angles that sum to 180 degrees, multiplying by the number of triangles gives the total sum of the interior angles.

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4) Each interior angle of a regular decagon measures:

Explanation

To find the measure of each interior angle of a regular decagon, you can use the formula: (n-2) × 180° / n, where n is the number of sides. For a decagon (n=10), the calculation is (10-2) × 180° / 10 = 144°.

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5) The number of diagonals in a polygon with n sides is:

Explanation

The formula for calculating the number of diagonals in a polygon is derived from the fact that each vertex can connect to (n-3) other vertices to form diagonals, and since each diagonal connects two vertices, the total is divided by 2.

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6) How many diagonals does a regular hexagon have?

Explanation

A regular hexagon has 9 diagonals, which can be calculated using the formula n(n-3)/2, where n is the number of sides (6 in this case). Thus, 6(6-3)/2 = 9.

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7) The central angle of a regular polygon with n sides is:

Explanation

The apothem is a line segment from the center of a regular polygon that is perpendicular to one of its sides, specifically connecting to the midpoint of that side.

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8) Each central angle of a regular nonagon measures:

Explanation

A regular nonagon has 9 sides, and the formula for calculating the central angle is (360°/number of sides). Thus, 360°/9 = 40°.

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9) In a regular polygon, the apothem connects the center to:

Explanation

The apothem is drawn from the center and meets the side at a right angle.

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10) The apothem of a regular polygon is always:

Explanation

The apothem of a regular polygon is the line segment from the center to the midpoint of one of its sides, and it is always perpendicular to that side.

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11) Which of the following regular polygons can tessellate the plane?

Explanation

These three have interior angles that fit exactly into 360°.

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12) A regular polygon with each exterior angle 24° has how many sides?

Explanation

The sum of the exterior angles of a polygon is always 360 degrees. To find the number of sides, you can divide 360 by the measure of each exterior angle. In this case, 360 / 24 = 15, so the polygon has 15 sides.

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13) Which statement is always true about a regular polygon?

Explanation

A regular polygon is defined as a polygon that is both equilateral (all sides are of equal length) and equiangular (all interior angles are equal). Therefore, Its sides are congruent and angles are congruent is the only statement that is universally true for all regular polygons.

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14) The sum of exterior angles of any polygon is:

Explanation

A regular polygon is defined as a polygon with all sides and angles equal. The sum of the interior angles of a polygon can be calculated using the formula (n-2) × 180°, where n is the number of sides. For regular polygons with 3 or more sides, the sum of angles will always be greater than 180°, and 360° is the angle sum for a quadrilateral, making it applicable to simple regular shapes like squares.

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15) The area of a regular polygon can be found using:

Explanation

The area of a regular polygon is calculated using the formula that relates the number of sides and the length of a side, typically involving the number 6 when using the apothem or side length in standard formulas.

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16) The area of a regular polygon can be found using:

Explanation

The formula for the area of a regular polygon involves the perimeter and the apothem, which is the distance from the center to the midpoint of a side. This formula is essential for calculating the area when the shape has equal sides and angles.

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17) A regular polygon has each central angle measuring 40°. how many sides does it have?

Explanation

The sum of all central angles in a polygon is 360 degrees. To find the number of sides (n), you can use the formula: n = 360 / central angle. Here, n = 360 / 40 = 9.

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18) Which regular polygon has each exterior angle equal to 72°?

Explanation

A regular pentagon has 5 sides, and the formula for calculating the measure of each exterior angle of a regular polygon is 360° divided by the number of sides. Thus, for a pentagon, 360°/5 = 72°.

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19) Which regular polygon has the fewest sides?

Explanation

A triangle is a polygon with three sides, which is the minimum number of sides required to form a polygon.

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20) The measure of each interior angle of a regular pentagon is:

Explanation

A regular pentagon has five sides. The formula to calculate the measure of each interior angle of a regular polygon is (n-2) × 180° / n, where n is the number of sides. For a pentagon, this becomes (5-2) × 180° / 5 = 108°.

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The sum of interior angles of a regular hexagon is:
The measure of each exterior angle of a regular octagon is:
The formula for the sum of interior angles of an n-sided polygon is:
Each interior angle of a regular decagon measures:
The number of diagonals in a polygon with n sides is:
How many diagonals does a regular hexagon have?
The central angle of a regular polygon with n sides is:
Each central angle of a regular nonagon measures:
In a regular polygon, the apothem connects the center to:
The apothem of a regular polygon is always:
Which of the following regular polygons can tessellate the plane?
A regular polygon with each exterior angle 24° has how many sides?
Which statement is always true about a regular polygon?
The sum of exterior angles of any polygon is:
The area of a regular polygon can be found using:
The area of a regular polygon can be found using:
A regular polygon has each central angle measuring 40°. how many...
Which regular polygon has each exterior angle equal to 72°?
Which regular polygon has the fewest sides?
The measure of each interior angle of a regular pentagon is:
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