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?
+166 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.
+166 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.
