Question

What is the sum of the measures of the interior angles of a regular polygon if each exterior angle measures 72°?

A. 1080°
B. 540°
C. 900°
D. 180°
E. 360°
F. 720​

Answer 1

The sum of the measures of the interior angles of a regular polygon can be found using the formula (n - 2) * 180 degrees, where n represents the number of sides. In this case, since each exterior angle measures 72°, each interior angle measures 180° - 72° = 108°. Using either formula, we find that the sum of the interior angles is 360°.

Step-by-step explanation:

To find the sum of the measures of the interior angles of a regular polygon, we can use the formula:

Sum of interior angles = (n - 2) * 180 degrees

where n represents the number of sides of the polygon. In this case, each exterior angle measures 72°, so each interior angle measures 180° - 72° = 108°.

Since the sum of the exterior angles of a polygon is always 360°, we can also use the formula:

Sum of interior angles = (n - 2) * 180 degrees = 360 degrees

Solving for n, we have:

n - 2 = 360/180 = 2

n = 4

Therefore, the sum of the measures of the interior angles of this regular polygon is:

Sum of interior angles = (4 - 2) * 180 degrees = 2 * 180 degrees = 360 degrees

Answer 2

B, 540 Degrees.

Step-by-step explanation:

If each exterior angle equals 72, then we know that the polygon has 5 sides, as the sum of the exterior angles of a polygon equals 360.

We also know that the interior angle is 108, and the exterior angle + the interior angle = 180.

Now, 108 * 5 = 540, meaning that the sum of the interior angles is 540 degrees.