Five fences meet at a point to form angles with measures x, 2x, 3x, 4x, and 5x around the point. Find the measure of each angle.
Five fences meet at a point to form angles with measures x, 2x, 3x, 4x, and 5x around the point. Find the measure of each angle.
To find the measure of each angle, we can use the fact that the sum of the measures of the angles around a point is always 360 degrees.
Let's set up an equation using this information:
x + 2x + 3x + 4x + 5x = 360
Combining like terms, we have:
15x = 360
To solve for x, we will divide both sides of the equation by 15:
x = 360 / 15
x = 24
Now, we can find the measure of each angle by substituting back into the given equation:
Angle 1 = x = 24 degrees
Angle 2 = 2x = 2 * 24 = 48 degrees
Angle 3 = 3x = 3 * 24 = 72 degrees
Angle 4 = 4x = 4 * 24 = 96 degrees
Angle 5 = 5x = 5 * 24 = 120 degrees
Therefore, the measure of each angle is:
Angle 1: 24 degrees
Angle 2: 48 degrees
Angle 3: 72 degrees
Angle 4: 96 degrees
Angle 5: 120 degrees
To find the measure of each angle, we need to use the fact that the sum of the angles around a point is always 360 degrees.
Let's add up the measures of the angles: x + 2x + 3x + 4x + 5x
This gives us a total of 15x.
Since the sum of the angles is 360 degrees, we can set up the equation:
15x = 360
To find the value of x, we need to solve this equation for x. Let's simplify the equation:
Divide both sides of the equation by 15:
x = 360 / 15
x = 24
Now that we have the value of x, we can substitute it back into the expression to find the measure of each angle:
Angle 1: x = 24 degrees
Angle 2: 2x = 2 * 24 = 48 degrees
Angle 3: 3x = 3 * 24 = 72 degrees
Angle 4: 4x = 4 * 24 = 96 degrees
Angle 5: 5x = 5 * 24 = 120 degrees
Therefore, the measure of each angle is:
Angle 1: 24 degrees
Angle 2: 48 degrees
Angle 3: 72 degrees
Angle 4: 96 degrees
Angle 5: 120 degrees