Let’s define:

• The number of sides of the smaller polygon as n.

• The number of sides of the larger polygon as 2n (since it has twice as many sides).

The sum of the exterior angles of any polygon is always 360°. Given that the larger polygon has a sum of exterior angles equal to 360°, this does not provide extra information to determine n.

The sum of the interior angles of a polygon with nn sides is given by:

Sum of interior angles=(n−2)×180°Sum of interior angles=(n−2)×180°

For the smaller polygon, we are given:

(n−2)×180°=540°(n−2)×180°=540°

Step 3: Solve for nn
(n−2)=540/180
n−2=3
n=5
Thus, the smaller polygon has 5 sides (a pentagon).

Since the larger polygon has twice as many sides:

2n=2×5=10

Thus, the larger polygon has 10 sides (a decagon).