The interior angles of a pentagon are in the ratio of 4 : 5 : 6 : 7 : 5. Find the smallest angle of the pentagon.

Sure, let's solve this step by step:

Step 1: Understand the problem We know that the interior angles of a pentagon are in the ratio of 4:5:6:7:5. We need to find the smallest angle.

Step 2: Recall the formula for the sum of interior angles of a polygon The sum of the interior angles of a polygon with n sides is given by the formula (n-2) * 180 degrees. For a pentagon (5 sides), this sum is (5-2) * 180 = 540 degrees.

Step 3: Find the total parts in the given ratio The ratio 4:5:6:7:5 adds up to 4 + 5 + 6 + 7 + 5 = 27 parts.

Step 4: Find the value of each part Each part in the ratio is equal to the total sum of the angles divided by the total number of parts. So, each part is 540 / 27 = 20 degrees.

Step 5: Find the smallest angle The smallest angle is represented by 4 parts in the ratio. So, the smallest angle is 4 * 20 = 80 degrees.

So, the smallest angle of the pentagon is 80 degrees.