A pentagon has sides so interior angle=(n-2)180/n where n=5Interior Angle = 108 degSum of external angles of any polygon is 360 degrees;So, 360/10=36 deg;3(36 degree)=108 degreeHence, Proved.

Introduction:
To prove that the interior angle of a regular five-sided polygon is three times the exterior angle of a regular decagon, we need to understand the properties of regular polygons and use their formulas.

Properties of a regular polygon:
1. A regular polygon has equal sides and equal interior angles.
2. The sum of the interior angles of a polygon can be found using the formula (n-2) * 180 degrees, where n is the number of sides of the polygon.
3. The sum of the exterior angles of any polygon is always 360 degrees.

Proving the statement:
Let's break down the proof into two parts:

Part 1: Interior angle of a regular five-sided polygon:
1. A regular five-sided polygon is called a pentagon.
2. Using the formula mentioned above, the sum of the interior angles of a pentagon is (5-2) * 180 = 540 degrees.
3. Since all interior angles of a regular polygon are equal, we divide the sum by the number of angles to find each interior angle: 540 / 5 = 108 degrees.

Part 2: Exterior angle of a regular decagon:
1. A regular decagon has ten sides and is composed of ten exterior angles.
2. Using the formula for the sum of exterior angles of any polygon, we have 360 degrees.
3. Since all exterior angles of a regular polygon are equal, we divide the sum by the number of angles to find each exterior angle: 360 / 10 = 36 degrees.

Comparing the interior angle of a pentagon with the exterior angle of a decagon:
1. We know that the interior angle of a pentagon is 108 degrees, and the exterior angle of a decagon is 36 degrees.
2. To prove the statement, we need to show that the interior angle of a pentagon is three times the exterior angle of a decagon.
3. Dividing the interior angle of a pentagon by the exterior angle of a decagon: 108 / 36 = 3.

Conclusion:
By comparing the interior angle of a regular pentagon (108 degrees) with the exterior angle of a regular decagon (36 degrees), we have proven that the interior angle of a regular five-sided polygon is three times the exterior angle of a regular decagon.