Mathematics

Polygons and Angles

102 Questions

Polygons and angles focus on calculating interior and exterior angle sums. Questions also cover properties of regular shapes like hexagons and nonagons. This geometry topic is essential for quantitative aptitude sections in major competitive exams.

Interior angle sumsExterior angle sumsRegular polygonsPolygon propertiesTriangle formation

Polygons and Angles Questions

Multiple choice

What is the name of the theorem that states that the sum of the interior angles of a polygon with n sides is (n-2) * 180 degrees?

  1. Brahmagupta's Theorem

  2. Bhaskara's Theorem

  3. Aryabhata's Theorem

  4. Varahamihira's Theorem
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Brahmagupta's Theorem states that the sum of the interior angles of a polygon with n sides is (n-2) * 180 degrees. This theorem is also known as the polygon angle sum formula.

Multiple choice

What is the name of the theorem that states that the sum of the exterior angles of a polygon is equal to 360 degrees?

  1. Brahmagupta's Theorem

  2. Pythagorean Theorem

  3. Euler's Formula

  4. Descartes' Theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Descartes' Theorem states that the sum of the exterior angles of a polygon is equal to 360 degrees.

Multiple choice

What is the name of the theorem that states that the sum of the exterior angles of a polygon is equal to 360 degrees?

  1. Brahmagupta's Theorem

  2. Pythagorean Theorem

  3. Euler's Formula

  4. Descartes' Theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Descartes' Theorem states that the sum of the exterior angles of a polygon is equal to 360 degrees.

Multiple choice

In Euclidean geometry, what is the sum of the interior angles of a triangle?

  1. 180 degrees

  2. 270 degrees

  3. 360 degrees

  4. 90 degrees
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of the interior angles of a triangle in Euclidean geometry is always 180 degrees, regardless of the size or shape of the triangle.

Multiple choice

The sum of the interior angles of a quadrilateral is always:

  1. 360 degrees

  2. 540 degrees

  3. 720 degrees
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of the interior angles of a quadrilateral is always 360 degrees.

Multiple choice

What is the name of the theorem that states that the sum of the exterior angles of a polygon is equal to 360 degrees?

  1. Pythagorean Theorem

  2. Brahmagupta's Theorem

  3. Euclid's Theorem

  4. Exterior Angle Theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Exterior Angle Theorem is a useful result for finding the sum of the exterior angles of a polygon.

Multiple choice

What is the name of the theorem that states that the sum of the exterior angles of a polygon is equal to 360 degrees?

  1. Pythagorean Theorem

  2. Brahmagupta's Theorem

  3. Euclid's Theorem

  4. Exterior Angle Theorem
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The Exterior Angle Theorem is a useful result for finding the sum of the exterior angles of a polygon.

Multiple choice

In geometry, what is a regular polygon with (n) sides called?

  1. Hexagon

  2. Pentagon

  3. Heptagon
  4. Regular \(n\)-gon
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A regular (n)-gon is a polygon with (n) sides of equal length and (n) interior angles of equal measure.

Multiple choice

What is the value of the sum of the exterior angles of a polygon with n sides?

  1. 180 degrees

  2. 270 degrees

  3. 360 degrees

  4. 450 degrees
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The sum of the exterior angles of a polygon with n sides is 360 degrees.

Multiple choice

What is the name of the theorem that states that the sum of the interior angles of a quadrilateral is equal to 360 degrees?

  1. Heron's formula

  2. Pythagorean theorem

  3. Brahmagupta's theorem

  4. Angle sum property of a quadrilateral
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The angle sum property of a quadrilateral is a result in geometry that establishes a relationship between the interior angles of a quadrilateral.

Multiple choice

What is the sum of the interior angles of a pentagon?

  1. 540°

  2. 720°

  3. 900°

  4. 1080°
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of the interior angles of a pentagon is always 540 degrees.

Multiple choice

What is the sum of the interior angles of a hexagon?

  1. 720°

  2. 900°

  3. 1080°

  4. 1260°
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of the interior angles of a hexagon is always 720 degrees.

Multiple choice

What is the sum of the interior angles of a heptagon?

  1. 900°

  2. 1080°

  3. 1260°

  4. 1440°
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of the interior angles of a heptagon is always 900 degrees.

Multiple choice

What is the sum of the interior angles of an octagon?

  1. 1080°

  2. 1260°

  3. 1440°

  4. 1620°
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of the interior angles of an octagon is always 1080 degrees.

Multiple choice

What is the sum of the interior angles of a nonagon?

  1. 1260°

  2. 1440°

  3. 1620°

  4. 1800°
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The sum of the interior angles of a nonagon is always 1260 degrees.