Interior Angle Practice

How many sides does a polygon have if the sum of its interior angles is 2160°? A. 14 B. 16 C. 18

A. 14 The sum = 2160, so 180 (n-2) =2160. Solve for n: 180(n-2) = 2160 180n - 360 = 2160 180n = 2520 n = 14

If the sum of the interior angles of a polygon equals 900°, how many sides does the polygon have? A. 7 B. 9 C. 10

A. 7 Explanation: The sum = 900, so 900 = 180 * (n-2). Solve for N. Step 1: 900 = 180n- 2(180) (distribute the 180) Step 2: 900 = 180n -390 (multiply 2 * 180) Step 3: 1260 = 180n (add 390 to both sides of the equal sign) Step 4: 1260/180 = 7; 180/180 = 1 (divide both sides by 180 to get n by itself) Step 5: N = 7

How many degrees are there in the sum of the interior angles of a nine sided polygon? A. 1080 B. 1260 C. 1620

B. 1260 degrees Explanation: Use the formula (N-2) * 180, where N is the number of sides. (9-2)*180 = 7*180= 1260

What is a polygon called if the sum of its interior angles equals 1440° ? A. Octagon B. Decagon C. Dodecagon

B. Decagon The sum = 1440, so 180(n-2)=1440. Solve for n: 180(n-2) = 1440 180n - 360 = 1440 180n = 1800 n = 10 Since the number of sides of the figure is 10 (n=10), the polygon is a decagon.

The sum of the interior angles of a hexagon equals: A. 360 B. 540 C. 720

C. 720 Degrees Explanation: A hexagon has 6 sides, so N = 6. So, apply the substitution method to the formula (N-2)180. (6-2) * 180 = 4 * 180 = 720