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One interior angle of a convex polygon (a convex polygon is a polygon where all anglesare less than 180 degrees) is 120 degrees. All the other angles are 130 degrees. How many sides does the polygon have?

 Jun 6, 2022

Best Answer 

 #1
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Let \(x\) be the number of sides in the polygon.

 

Using what we are given, we get the equation \(120+130(x-1)=180(x-2)\).

 

Expanding, we have \(120+130x-130=180x-360\). Then, by moving all the terms to the left and combining like terms, the equation turns into \(-50x+350=0\).

 

Therefore, the polygon has \(\fbox{7}\) sides.

 Jun 7, 2022
 #1
avatar+68 
+1
Best Answer

Let \(x\) be the number of sides in the polygon.

 

Using what we are given, we get the equation \(120+130(x-1)=180(x-2)\).

 

Expanding, we have \(120+130x-130=180x-360\). Then, by moving all the terms to the left and combining like terms, the equation turns into \(-50x+350=0\).

 

Therefore, the polygon has \(\fbox{7}\) sides.

RainbowSquirrel53 Jun 7, 2022

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