In a convex polygon measurement of interior angles in an A.P where the smallest interior angle is 60 and the largest interior angle is 120 what are the interior angles of the polygon
Let the number of sides of the convex polygon be n.
Since the interior angles are in an arithmetic progression (A.P), we can say that the common difference is d.
Given that the smallest interior angle is 60 and the largest interior angle is 120, we have:
First term, a = 60
Last term, l = 120
We know that the sum of the interior angles of a polygon can be calculated using the formula:
Sum of interior angles = (n-2) x 180
Also, for an A.P, the sum of the angles can be calculated using the formula:
Sum = n/2 x (First term + Last term)
Equating the two formulas, we have:
(n-2) x 180 = n/2 x (60 + 120)
180n - 360 = 90n
90n = 360
n = 4
Therefore, the polygon is a quadrilateral with 4 sides.
We can find the common difference (d) using the formula:
d = (Last term - First term) / (n - 1)
d = (120 - 60) / (4 - 1)
d = 60 / 3
d = 20
So, the interior angles of the polygon with 4 sides are:
60, 80, 100, 120