An angle of a pentagon is 120° . The other angles are equal to one another . Find the size of one of the other angles .
Let's call the size of the other angles x.
We know that a pentagon has five angles, so we can use the formula for the sum of the angles in a polygon:
Sum of angles = (n-2) x 180 degrees
where n is the number of sides
For a pentagon, n = 5:
Sum of angles = (5-2) x 180 degrees
Sum of angles = 3 x 180 degrees
Sum of angles = 540 degrees
We also know that one of the angles is 120 degrees:
Sum of other four angles + 120 degrees = 540 degrees
Subtracting 120 degrees from both sides:
Sum of other four angles = 420 degrees
Since the other angles are equal to one another:
4x = 420
Dividing both sides by 4:
x = 105
Therefore, the size of one of the other angles is 105 degrees.
To find the size of one of the other angles in the pentagon, we need to use the formula for the sum of the interior angles of a polygon.
The formula for the sum of the interior angles of an n-sided polygon is given by:
Sum = (n-2) * 180°
Since we are dealing with a pentagon (n = 5), we can apply this formula:
Sum = (5 - 2) * 180°
Sum = 3 * 180°
Sum = 540°
We know that one angle is 120°, so we can subtract this angle from the sum to find the sum of the other four angles:
Sum of other four angles = 540° - 120°
Sum of other four angles = 420°
To find the size of one of the other angles, we need to divide this sum by 4:
Size of one of the other angles = 420° / 4
Size of one of the other angles = 105°
Therefore, one of the other angles in the pentagon is 105°.