Match each polygon description based on its angle properties to the correct geometric shap… — Armed Services Vocational Aptitude Battery (ASVAB)

Match each polygon description based on its angle properties to the correct geometric shape.

A polygon where the sum of the interior angles is $540^\circ$ .Pentagon
A regular polygon where each individual interior angle measures $120^\circ$ .Regular Hexagon
A polygon in which the sum of the interior angles equals $1080^\circ$ .Octagon
A polygon whose interior angle sum exactly equals its exterior angle sum.Quadrilateral

Match the

540^\circ

sum to Pentagon, the

120^\circ

interior angle to Regular Hexagon, the

1080^\circ

sum to Octagon, and the equal interior/exterior sums to Quadrilateral.

Each match correctly applies the sum of interior angles formula,

S = (n-2) \times 180^\circ

, or relies on the fact that the sum of exterior angles for any convex polygon is exactly

360^\circ

. Solving for

n

reveals the specific polygon.

Find the number of sides for a polygon with a

540^\circ

interior angle sum.

n = 5

We apply the formula

(n-2) \times 180 = 540

, which simplifies to

n-2 = 3

Determine the number of sides for a regular polygon with a

120^\circ

interior angle.

n = 6

The exterior angle is

180^\circ - 120^\circ = 60^\circ

. The number of sides is

360^\circ / 60^\circ = 6

Find the number of sides for a polygon with a

1080^\circ

interior angle sum.

n = 8

Applying the formula gives

(n-2) \times 180 = 1080

, which simplifies to

n-2 = 6

Identify the polygon where the interior angle sum equals the exterior angle sum.

n = 4

Since the exterior sum is always

360^\circ

, we set

(n-2) \times 180 = 360

, yielding

n-2 = 2

Polygon Interior and Exterior Angle Formulas

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