Two angles of a polygon are right angles & the remaining are 120 degrees each. Find the number of other sides in in it.
two exterior angles are also 90°
The remaining exterior angles (all the same), are 180-120 = 60°
The exterior angles add to 360°, so there are 3 more of them, each 60°.
The figure is a pentagon similar to a home plate in baseball.
Consider that the interior angles of a hexagon are all 120°. Drawing a diagonal between two adjacent sides will form this figure.
To find the number of sides in the polygon, we can use the fact that the sum of the interior angles of a polygon with n sides is given by the formula (n - 2) * 180 degrees.
In this case, we know that two angles of the polygon are right angles, which means they measure 90 degrees each. The remaining angles are all 120 degrees each.
Let's denote the number of sides of the polygon as n. We can set up the equation:
2 * 90 + (n - 2) * 120 = (n - 2) * 180
Simplifying this equation gives us:
180 + 120(n - 2) = 180(n - 2)
Now, let's solve for n:
180 + 120n - 240 = 180n - 360
Combine like terms:
120n - 60 = 180n - 360
Subtracting 120n from both sides:
-60 = 60n - 360
Adding 360 to both sides:
300 = 60n
Dividing both sides by 60:
n = 5
Therefore, the polygon has 5 sides.