Answer to Question #154092 in Geometry for Janine Leodones

Question #154092

How many sides has a regular polygon if the measure of one of its angles is 128 4/7º? 144º? 160º?


1
Expert's answer
2021-01-06T19:49:30-0500

For a regular polygon, let "n" be the number of sides and "\\alpha" be the interior angle.

The sum of interior angles for a regular polygon is "n\\alpha" .

Also we can use another formula for calculating the sum of interior angles: "180^\\circ (n-2)" .

"180^\\circ (n-2)=n\\alpha\n\\\\\n180^\\circ n-360^\\circ =n\\alpha \n\\\\\nn(180^\\circ -\\alpha )=360^\\circ \n\\\\\nn=\\frac{360^\\circ}{180^\\circ -\\alpha }"


1) "\\alpha =128 \\ 4\/7 ^\\circ"

"n=\\frac{360^\\circ}{180^\\circ -128\\ 4\/7^\\circ }=\\frac{360^\\circ}{51\\ 3\/7^\\circ}=7"


2) "\\alpha =144 ^\\circ"

"n=\\frac{360^\\circ}{180^\\circ -144^\\circ }=\\frac{360^\\circ}{36^\\circ}=10"


3) "\\alpha =160^\\circ"

"n=\\frac{360^\\circ}{180^\\circ -160^\\circ }=\\frac{360^\\circ}{20^\\circ}=18"


Answer: 7 sides; 10 sides; 18 sides.


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS