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Question

Difficulty: EasyQuadrilaterals and Polygons

A decorative floor tile is manufactured in the shape of a regular pentagon. What is the degree measure of each interior angle of the tile?

  1. A
    72∘72^\circ
  2. 108∘108^\circAnswer
  3. C
    180∘180^\circ
  4. D
    540∘540^\circ

Answer

108∘108^\circ
The interior angles of an nn-sided polygon sum to (n−2)×180∘(n - 2) \times 180^\circ. For a 5-sided pentagon, the sum is (5−2)×180∘=540∘(5 - 2) \times 180^\circ = 540^\circ. Since the tile is a regular pentagon, all five angles are identical. Dividing the total 540∘540^\circ by 5 yields exactly 108∘108^\circ per corner.

Step-by-Step Solution

1
Identify the number of sides in a regular pentagon.
n=5n = 5
A pentagon is defined as a geometric polygon with exactly 5 sides.
2
Calculate the sum of all interior angles using the polygon formula (n−2)×180∘(n - 2) \times 180^\circ.
(5−2)×180∘=3×180∘=540∘(5 - 2) \times 180^\circ = 3 \times 180^\circ = 540^\circ
This formula determines the total degree measure for the interior angles of any convex polygon.
3
Divide the total sum by the number of sides to find the measure of a single interior angle.
540∘÷5=108∘540^\circ \div 5 = 108^\circ
Because it is a regular pentagon, all interior angles are equal in measure.

Key Concept

Interior Angles of Regular Polygons
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Topics

Quadrilaterals and Polygons

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