Question

If a figure has n number of congruent angles and the sum of the angles is 1080°, how many sides does the figure have? What is the name of the figure? Show all work in solving the problem. Use the formula Sum=(n-2)180° to solve the problem.

A) The figure has 10 sides and is called a decagon.
B) The figure has 12 sides and is called a dodecagon.
C) The figure has 9 sides and is called a nonagon.
D) The figure has 8 sides and is called an octagon.

Answer 1

Using the formula 1080° = (n-2) × 180°, we solve for n to find that the figure is an octagon, which has 8 sides.

Step-by-step explanation:

To determine the number of sides a figure has if it has congruent angles and the sum of the angles is 1080°, we use the formula Sum = (n-2) × 180°, where n is the number of sides. Let's solve the equation:

1080° = (n-2) × 180°

To find n, we divide both sides by 180°:

6 = n - 2

Adding 2 to both sides gives us:

n = 8

The figure with 8 sides is called an octagon. Thus, the correct answer is D) The figure has 8 sides and is called an octagon.