Suppose the interior angles of a convex pentagon are five consecutive numbers, find the measure of the largest

Question

Suppose the interior angles of a convex pentagon are five consecutive numbers, find the measure of the largest angle.

Plz support your answer

Answer 1

The sum of the angles of a convex n-gon is given by the formula:

S = 180(n - 2), where n is the number of the vertices.

So for a convex pentagon we have:

S = 180(5 - 2) = 540 degrees.

Now if x1 is the smallest angle, x2 is the next etc, we have:

x2 = x1 + 1, x3 = x1 + 2, x4 = x1 + 3, x5 = x1 + 4

but

x1 + x2 + x3 + x4 + x5 = 540, so:

x1 + x1 + 1 + x1 + 2 + x1 + 3 + x1 + 4 = 540

5x1 + 10 = 540

5x1 = 530

x1 = 106 degrees

and at last

x4 (the largest) = x1 + 4 = 106 + 4 = 110 degrees