The measure of each interior angle of a regular is 8 times that of an exterior angle. How many sides does the polygon have?

Answer 1

n the 1960's, Seymour Papert and a team at MIT created Turtle Graphics and the Logo programming language to teach computer programming to kids. The program controlled a "Turtle" that could draw. It had operations like "Pen Down" and "Move 10"" and "Left 20."

Now, if the Turtle turned left 20° N times it would draw a regular polygon and return to its original position facing in the original direction, having turned 360°.

So, since the exterior angle is 20°, this regular polygon had 360°/20° = 18 sides.

e.g., Google "logointerpreter"

Answer 2

Recall that the interior and exterior angle of a polygon is supplementary, meaning they add up to 180°. If we refer to the interior angle as I and the exterior angle as E, then:

I + E = 180

Since the interior angle is 8 times that of an exterior angle,

(8E) + E = 180 [replacing I with 8E]

9E = 180 [combining like terms]

E = 20 [divide both sides by 9]

So the exterior angle of this polygon is 20 degrees. Using this value,

I + E = 180 [Given]

I + 20 = 180 [replacing E with 20]

I = 160 [subtract 20 from both sides]

The interior angle of this polygon is 160 degrees.

The equation to find the interior angle of a polygon with n sides is:

I = ( (n − 2) × 180 ) ⁄ n

Since we know the interior angle, we can plug it in and solve for n, the number of sides in the polygon:

160 = ( (n − 2) × 180 ) ⁄ n [Given, plugging in 160 for I]

160n = (n − 2) × 180 [multiply both sides by n]

160n = 180n − 360 [distribute 180 to (n - 2)]

-20n = -360 [bring all n values to the left side]

n = 18 [divide both sides by -20]

Therefore, the polygon has 18 sides.

Answer 3

each interior angle plus its exterior angle sums to 180°

x=measure of an exterior angle

8x=measure of an interior angle

8x+x=180

9x=180

x=20°

8*20=160° for each interior angle

the total number of degrees in a regular polygon is given by the formula (n-2)(180) where n=# of sides of the polygon

the number of sides equals the number of angles

(n-2)(180)=160*n

180n-360=160n

180n-160n=360

20n=360

n=360/20

n=18 sides

the polygon has 18 sides

check: (n-2)(180)=(18-2)(180)=16*180=2880° in the polygon

there are 18 sides

2880/18=160° for each interior angle which was determined above