Three angles of a hexagon are congruent. The other three angles are also congruent, each with a measure twice that of the first three. What is the measure of each angle?
To find the measure of each angle of the hexagon, we can start by finding the measure of one angle.
Let's assume the measure of one angle is "x" degrees.
According to the information given, three angles of the hexagon are congruent. So, the sum of these three angles would be 3 times the measure of one angle: 3x degrees.
The other three angles are also congruent, each with a measure twice that of the first three. So, the measure of each of these angles would be 2 times the measure of one angle: 2x degrees.
To find the total sum of the six angles in a hexagon, we can add up the measures of all the angles:
3x + 2x + 2x + 3x + 2x + 2x = 12x degrees
Since the sum of all angles in a hexagon is 720 degrees (a hexagon has six angles and the sum of all angles is (6-2) * 180 degrees), we can set up an equation:
12x = 720
Now, we can solve this equation to find the value of "x":
12x = 720
x = 720 / 12
x = 60
Therefore, the measure of each angle in the hexagon is 60 degrees.