# The angles of a convex polygon are 2: 3: 4: 5: 6. Find the largest of the angles.

January 15, 2021 | education

| Let’s use the formula for determining the sum of the interior angles of a convex polygon – (n – 2) * 180, where n is the number of angles of the polygon.

∑ = (5 – 2) * 180 = 540.

Let one part of the angle of the polygon be equal to X degrees, then:

2 * X + 3 * X + 4 * X + 5 * X + 6 * X = 540.

20 * X = 540.

X = 540/20 = 27.

One part of the angle is 27.

The largest angle of the polygon is the angle with the largest ratio, then 6 * 27 = 162.

Answer: The largest angle of the polygon is 162.

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