Question

What is the sum of 7 of the interior angles of a regular decagon?

Answer 1

Answer:

The answer is 1008 degrees

Step-by-step explanation:

Answer 2

The sum of 7 of the interior angles of a regular decagon is 1008°.

What is interior angle of polygon?

• It is an angle inside a shape.
• All the interior angles in a regular polygon are equal.

Formula to find the sum of interior angles of a polygon:

S = (n - 2) × 180°, where n is the number of sides of the regular polygon.

What is decagon?

"It is a polygon having ten sides, ten interior angles and ten vertices."

For given example,

We need to find the sum of 7 of the interior angles of a regular decagon.

Number of sides of decagon (n) = 10

Using the formula of sum of interior angles,

⇒ S = (n - 2) × 180°

⇒ S = (10 - 2) × 180°

⇒ S = 1440°

This means the sum of all interior angles of a regular decagon is  1440°.

We know, there are 10 interior angles of regular decagon.

Let  'x' represents the measure of each interior angle of a regular decagon.

⇒ 10x = 1440°

⇒ x = 1440/10

⇒ x = 144°

This means, the interior angle of a regular decagon measures 144°

So, the sum of 7 of the interior angles would be,

7 × 144° = 1008°

Therefore, the sum of 7 of the interior angles of a regular decagon is 1008°.

Learn more about the interior angles of a regular decagon here:

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