An angle of a pentagon is 120° . The other angles are equal to one another . Find the size of one of the other angles .

Answer 1

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.