The sum of the four angles of a convex pentagon is 460 °. Find the fifth corner.

It is known from the condition that the sum of the four angles of a convex pentagon is 460 °. We need to find the degree measure of the fifth angle.

Let’s start by recalling the formula for calculating the degree measure of the angles of a convex n-gon:

180 ° * (n – 2).

Let’s calculate the sum of the angles of a convex 5-gon:

180 ° * (5 – 2) = 180 ° * 3 = 540 °.

We know the sum of the four angles of the pentagon from the condition and it is equal to 460 °, and in order to find the fifth angle, we will subtract the sum of 4 angles from the sum of all angles:

540⁰ – 460⁰ = 80⁰.