Question

If each interior angle of a regular convex polygon is three times the measure of each exterior angle , what kind of polygon is it ? _______

Answer 1

@samsterz @Cookie_009 anyone know how I can figure this one out ?

Answer 2

Can you take that drawing and show an exterior angle?

Answer 3

I know where the exterior angle would be , but idk how to draw on that picture ..

Answer 4

Take my picture, and click on the little pencil icon on the top right.
Click on the third icon from the left on the top, do draw a line.
Then insert the drawing and post the response.

Answer 5

Seems I have the answer right now.

Answer 6

Ok, I did it for you.

Answer 7

there is the one that i drew.

Answer 8

Now look at the exterior angle and interior angle above. I'm going to label them with the given inoformation.

Answer 9

Great, that's correct.

Answer 10

The given info is that the measure of each interior angle is 3 times the measure of each exterior angle. If we let the exterior angle have measure x, then the interior angle has measure 3x. Ok?

Answer 11

Now I'll add that to my picture.

Answer 12

Yes . I understand so far . and the exterior measures have to sum up to 360 and the interior angles have to add up to 180.

Answer 13

Now, can you look at the labeled angles. What kind of angles are they?

Answer 14

Okay so would you divide 180 by 3 ?

Answer 15

An interior angle of a polygon and an adjacent exterior angle are supplementary angles.

Answer 16

Not quite.
The angles have measures x and 3x. they are supplementary, that means
x + 3x = 180

Answer 17

if you add like terms then wouldn't you get 4x=180 ?

Answer 18

Correct. Now you can solve for x.

Answer 19

it will be a decimal number . but how can i figure out what kind of polygon is being discussed ?

Answer 20

No, it's not a decimal number. It's a whole number.
Divide 180 by 4. What do you get?

Answer 21

For a polygon each interior angle equals
(# sides -2) * 180 / # sides

Answer 22

@mathstudent55 it is 45 , i am sorry I did my dividing wrong .

Answer 23

\( 4x = 180\)

Divide both sides by 4:

\(\dfrac{4x}{4} = \dfrac{180}{4} \)

\( x = 45\)

Answer 24

Great. x = 45.
Remember that x is the measure of the exterior angle, so we have a regular polygon with an exterior angle measure of 45 degrees.

Answer 25

so now we have to mutiply 3 and 45 to find the measure of the interior angles right ?

Answer 26

No need. We'll use the exterior angle to find the number of sides.

You wrote above that the sum of the measures of the exterior angles of a polygon is 180. If all angles add to 180, and one angle is 45, how many angles do you have?

Answer 27

exterior angles equal 360 not 180 but wont I still do that same thing ?

Answer 28

@mathstudent55 i got that it is an octagon . @wolf1728 do you agree ?

Answer 29

Yes.

Answer 30

Sorry, I meant 360.
360/45 = 8. That shows 8 sides. It's an octagon. You are correct.

Answer 31

@mathstudent55 can you help me with one more question ?

Answer 32

Sure.

Answer 33

@Faith_Rochelle
Above you wrote
"Yes . I understand so far . and the exterior measures have to sum up to 360 and the interior angles have to add up to 180."

Answer 34

A baseball's diamond home plate has three right angles. The remaining two angles are congruent. What are their measures ? _________ @mathstudent55

Answer 35

You are correct that the measures of exterior angles add to 360, but the measures of the interior angles only add to 180 in a triangle. In a polygon with more sides the sum is a larger number.

Answer 36

@wolf1728 wrote the formula above.

For a polygon of n sides, the sum of the measures of the interior angles is:
(n - 2)180

Answer 37

N would = 5 right ?

Answer 38

Let's draw it first.

Answer 39

Ok (:

Answer 40

Yes. Use n = 5 to find the sum of the measures of the angles.

Answer 41

(5-2)180 @mathstudent55 that would be 3x180 and that equals 540.

Answer 42

Correct. The sum is 540.