The sum of angles of an octagon is 750.Three angles are equal.Calculate the sides of the equal angles
hmmm. The sum of the angles of an octagon is 6*180 = 1080
and knowing the angles gives no information about the sides.
Bzzzt. But thanks for playing.
Please
To find the measure of the equal angles in an octagon, we can use the fact that the sum of the angles in an octagon is 1080 degrees.
Given that the sum of angles is 750 degrees, we subtract this from 1080 to find the measure of the remaining angles:
1080 - 750 = 330 degrees
We know that three of the angles are equal, so we divide the remaining measure by 3 to find the measure of each of the equal angles:
330 / 3 = 110 degrees
Therefore, the measure of each of the equal angles in the octagon is 110 degrees.
To calculate the sides of the equal angles in an octagon, we need to first determine the measure of each angle.
An octagon has 8 angles. Let's represent the measure of each angle as "x."
Given that the sum of the angles of the octagon is 750 degrees, we can use the formula for the sum of angles in a polygon to solve for x:
Sum of angles = (n - 2) * 180
where "n" is the number of sides in the polygon.
For an octagon, n = 8. Therefore,
750 = (8 - 2) * 180
750 = 6 * 180
750 = 1080
Now, we can solve for x by dividing the total sum of the angles by the number of angles:
x = 1080 / 8
x = 135
So, each angle in the octagon measures 135 degrees.
Since we know that three angles are equal, we can calculate the sides of these angles by using properties of regular polygons. In a regular octagon, all sides and angles are equal.
The formula to calculate the measure of each interior angle in a regular polygon is:
Interior angle = (n - 2) * 180 / n
where "n" is the number of sides.
For an octagon, n = 8. Therefore,
Interior angle = (8 - 2) * 180 / 8
Interior angle = 6 * 180 / 8
Interior angle = 135
So, each interior angle in a regular octagon measures 135 degrees, and therefore, the sides of the equal angles in the given octagon would also be equal.