three angles of a nonagon are equal and the sum of six other angles are 960°.calculate the size of the equal angles.
since their sum is (9-2)*180 = 1260, the unknown angles of x degrees each can be found via
3x + 960 = 1260
now just find x.
To find the size of the equal angles in a nonagon, we need to first determine the total sum of angles in a nonagon, which will help us find the value of each angle.
A nonagon has 9 sides, so it will have 9 angles. The sum of all the angles in any polygon can be calculated using the formula: (n−2) × 180°, where "n" represents the number of sides.
For a nonagon, the sum of all the angles is calculated as follows:
(9−2) × 180°
= 7 × 180°
= 1260°
Now, we know that three angles of the nonagon are equal, so let's assume the size of these angles to be "x". This means that the sum of these three angles will be 3x.
Additionally, the sum of the remaining six angles is given as 960°.
To set up an equation and solve for the value of "x", we can equate the total sum of all angles to the sum of the equal angles and the sum of the remaining six angles:
3x + 960° = 1260°
Now, let's solve this equation for "x":
3x = 1260° - 960°
3x = 300°
x = 300° ÷ 3
x = 100°
Therefore, the size of each of the equal angles in the nonagon is 100°.