Question

The angels of a triangle have a sum of 180°. The angles of a rectangle have a sum of 360°. The angels of a pentagon have a sum of 540°. Continue this pattern to find the sum of the angles of an octagon

Answer 1

Explanation:

It is given that the angels of a triangle have a sum of 180°. The angles of a rectangle have a sum of 360°. The angels of a pentagon have a sum of 540.

Let me define the each terms.

1. We know that each angle in a triangle is 60°, So there is a three angle in a regular triangle.

• 60° + 60° + 60°
• 180°

2. We know that each angle in a rectangle, is 90°, So there is a four angle in a regular rectangle.

• 90° + 90°+90°+90°
• 360°

Similarly,

• There is 8 angle in a regular octagon and each angle measurement is 135°.

So, sum of the angles of an octagon = 135° × 8

Sum of the angles of an octagon = 1080°

Therefore, the required sum of the angles of an octagon is 1080°