The size of an interior angle of a regular polygon is 3x° while its exterior angle is (x- 20)°. Find the number of sides of the polygon
first let's find value of x where
3x°+(x-20)°=180°
3x +x -20 =180
4x=180+20
4x=200
4x/4=200/4
x=50°
then number of sides = 360/(exterior angle)
of a regular polygony
therefore sizes=360/30
sides= 12
7.2
12
Well, it seems this polygon is playing mind games with us, changing its angles and all. Let's not fall for its tricks and solve this riddle.
In any polygon, whether regular or not, an interior angle and its corresponding exterior angle add up to 180 degrees. So, we have the equation:
(3x) + (x - 20) = 180
Now let's solve this equation:
3x + x - 20 = 180
4x - 20 = 180
4x = 200
x = 50
Since x represents the interior angle, we can find the exterior angle by substituting 50 into (x - 20):
Exterior angle = 50 - 20 = 30 degrees
Now, we know that the exterior angle of a regular polygon is always 360 divided by the number of sides. So, we can set up another equation:
30 = 360 / n
Solving for n, the number of sides of our sneaky polygon:
30n = 360
n = 360 / 30
n = 12
Voila! Our polygon has 12 sides. Keep an eye out for any more tricks it might have up its sleeve!
To find the number of sides of the polygon, we need to use the relationship between interior and exterior angles of a regular polygon.
In a regular polygon, the sum of the interior angles is given by the formula (n-2) * 180°, where n represents the number of sides of the polygon.
Given that the size of an interior angle is 3x° and the size of an exterior angle is (x - 20)°, we can set up the following equation:
3x + (x - 20) = (n-2) * 180
Simplifying the equation:
4x - 20 = (n-2) * 180
Now, let's solve for n, the number of sides:
Divide both sides of the equation by 180:
(4x - 20) / 180 = (n - 2)
Simplifying further:
4x - 20 = 180n - 360
Rearranging terms:
180n = 4x - 20 + 360
180n = 4x + 340
Divide both sides by 180:
n = (4x + 340) / 180
Simplifying:
n = 2x/45 + 34/9
Therefore, the number of sides of the polygon is given by the expression (2x/45) + (34/9).