Polygon Angle Puzzler

Imagine Jackson, Henry, and Liam are on a magical quest in a mystical land. They stumble upon a secret door shaped like a pentagon. To unlock it, they need to figure out the sum of the interior angles of a pentagon. Can you help them?

• 540 degrees

• 720 degrees

• 360 degrees

• 180 degrees

Answer explanation

The sum of the interior angles of a pentagon is always 540 degrees, which is the correct choice.

Isla, Daniel, and Harper are on a thrilling adventure to build a model of a magical hexagonal castle for their school project. They need to figure out the sum of its interior angles. If they transform the hexagon into a series of triangles, how many mystical triangles will they end up with?

• 4

• 5

• 6

• 3

Answer explanation

To find the sum of interior angles, they need to divide the hexagon into triangles. Since a hexagon has 6 sides, they will end up with 6 triangles. Therefore, the correct choice is 6.

Olivia, Aria, and Abigail are playing a game of 'Shape Masters'. They come across a regular octagon and Olivia notices that one of its interior angles is 135 degrees. Aria challenges Abigail to find out the sum of all interior angles of the octagon. Can you help Abigail win the challenge?

• 960 degrees

• 1080 degrees

• 1200 degrees

• 1088 degrees

Answer explanation

The sum of all interior angles of a regular octagon is given by the formula (n-2) * 180 degrees, where n is the number of sides. In this case, the sum is (8-2) * 180 = 1080 degrees. Therefore, the correct answer is 1080 degrees.

Imagine Jackson, Evelyn, and David are on a quest to find a hidden treasure. They stumble upon a door with a regular dodecagon (12-sided polygon) and a riddle that says 'The key to open this door lies in the measure of each interior angle of this shape'. What is the measure they should consider?

• 150 degrees

• 160 degrees

• 170 degrees

• 180 degrees

Answer explanation

The measure they should consider is 150 degrees because it is the correct answer choice.

A polygon has 9 sides. What is the sum of the measures of its interior angles?

• 1260 degrees

• 1400 degrees

• 1440 degrees

• 1620 degrees

Answer explanation

The sum of the measures of the interior angles of a polygon with 9 sides is 1260 degrees, which is the correct choice.

How many degrees are in each interior angle of a regular pentagon?

• 108 degrees

• 120 degrees

• 128 degrees

• 135 degrees

Answer explanation

Each interior angle of a regular pentagon measures 108 degrees, making it the correct choice.

What is the sum of the interior angles of a 14-sided polygon?

• 2160 degrees

• 2340 degrees

• 2520 degrees

• 1800 degrees

Answer explanation

The sum of the interior angles of a polygon with n sides is given by the formula (n-2) * 180 degrees. Therefore, for a 14-sided polygon, the sum of the interior angles is (14-2) * 180 = 2160 degrees. Thus, the correct answer is 2160 degrees.

If a polygon has 20 sides, what is the measure of each interior angle if it is a regular polygon?

• 156 degrees

• 162 degrees

• 168 degrees

• 174 degrees

Answer explanation

The measure of each interior angle of a regular polygon with 20 sides is 174 degrees, which is the correct choice.

A nonagon (9-sided polygon) has one interior angle that measures 140 degrees. If the polygon is regular, what is the measure of each of the other interior angles?

• 140 degrees

• 120 degrees

• 160 degrees

• 135 degrees

Answer explanation

In a regular nonagon, all interior angles are equal. Since one angle measures 140 degrees, each of the other interior angles also measures 140 degrees.

What is the sum of the interior angles of a 25-sided polygon?

• 4140 degrees

• 4320 degrees

• 4500 degrees

• 4680 degrees

Answer explanation

The sum of the interior angles of a polygon can be found using the formula (n-2) * 180, where n is the number of sides. For a 25-sided polygon, the sum is (25-2) * 180 = 4140 degrees. Therefore, the correct answer is 4140 degrees.