If the size of the interior angles of a pentagon are 2x , 3x , 4x , 5x and 6x , find the largest angle of the pentagon
To find the largest angle of the pentagon, we need to determine the value of x first.
We can use the fact that the sum of the interior angles of any polygon is (n-2) * 180 degrees, where n is the number of sides of the polygon.
In this case, we have a pentagon, which means n = 5.
So, the sum of the interior angles of the pentagon is (5-2) * 180 = 3 * 180 = 540 degrees.
The given angles in terms of x are 2x, 3x, 4x, 5x, and 6x.
We can add these angles together and set it equal to the sum of the interior angles.
2x + 3x + 4x + 5x + 6x = 540
20x = 540
Dividing both sides by 20, we get:
x = 540/20
x = 27
Now that we know the value of x, we can substitute it into the expressions for the angles.
The largest angle is 6x, so substituting x = 27, we have:
6 * 27 = 162 degrees.
So, the largest angle of the pentagon is 162 degrees.
To find the largest angle of the pentagon, we need to determine the value of x.
In any polygon, the sum of the interior angles is given by the formula (n - 2) * 180 degrees, where n represents the number of sides or angles in the polygon.
For a pentagon, n = 5, so the sum of the interior angles is (5 - 2) * 180 = 3 * 180 = 540 degrees.
We can set up an equation using the given information about the size of the angles:
2x + 3x + 4x + 5x + 6x = 540
Combine like terms:
20x = 540
Divide both sides by 20 to solve for x:
x = 540 / 20
x = 27
Now that we know x, we can substitute it back into the expressions for the angle sizes to find the largest angle:
6x = 6 * 27 = 162 degrees
Therefore, the largest angle of the pentagon is 162 degrees.
20x÷450= 27
well, they total to 540, so just solve
20x = 540
and go from there