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

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.