In a nonagon, six of the angles are equal, and each of the other three angles is 33degree more than each of the six angles.Find the angles.
the sum of the internal angles of a nonagon is ... (9 * 180º) - 360º
6 a + [3 * (a + 33)] = (9 * 180º) - 360º
To find the angles of a nonagon with the given conditions, we can start by determining the measure of the six equal angles.
Let's represent the measure of each of the six equal angles as x.
So, each of the three remaining angles is 33 degrees more than each of the six equal angles. This means the measures of these three angles are (x + 33), (x + 33), and (x + 33).
Next, we can use the fact that the sum of the angles in a nonagon is 1440 degrees. Since all the angles in a nonagon are equal, we can set up the equation:
6x + (x + 33) + (x + 33) + (x + 33) = 1440
Simplifying the equation:
6x + 3x + 99 = 1440
9x = 1440 - 99
9x = 1341
x = 1341 / 9
x = 149
Now that we have the value of x, we can substitute it back into the expressions for the angles:
Angle 1: x = 149 degrees
Angle 2: x + 33 = 149 + 33 = 182 degrees
Angle 3: x + 33 = 149 + 33 = 182 degrees
So, the angles in the nonagon are:
Angle 1: 149 degrees
Angle 2: 182 degrees
Angle 3: 182 degrees
Angle 4: 149 degrees
Angle 5: 149 degrees
Angle 6: 149 degrees
Angle 7: 182 degrees
Angle 8: 182 degrees
Angle 9: 149 degrees