Examples on Interior Angles
Example 1: What is the sum of interior angles of a polygon with 10 sides?
Solution:
Sum of Interior Angles of a Polygon = (n – 2) × 180°
Sum of interior angles of a polygon with 10 sides = (10 – 2) × 180°
Sum of interior angles of a polygon with 10 sides = 8 × 180°
Sum of interior angles of a polygon with 10 sides = 1440°
Example 2: If the exterior angle of a polygon is 105° then, find the measure of interior angle of polygon.
Solution:
Exterior angle of a polygon = 105°
To find the measure of interior angle we use the formula.
Interior Angle of Polygon = 180° – Exterior Angle of polygon
Interior angle of Polygon = 180° – 105°
Interior angle of Polygon = 75°
Example 3: Find the interior angle x of below given polygon.
Solution:
As the given figure is a quadrilateral and we know that,
Sum of Interior Angles of a Quadrilateral = 360°
100° + 70° + 160° + x = 360°
x + 330° = 360°
x = 360° – 330°
x = 30°
Measure of interior angle x of given irregular polygon = 30°
Example 4: Find the interior angle of a regular polygon with 6 sides.
Solution:
Sum of Interior Angles of a Polygon = (n – 2) × 180°
Sum of interior angles of a regular polygon with 6 sides = (6 – 2) × 180°
Sum of interior angles of a regular polygon with 6 sides = 4 × 180°
Sum of interior angles of a regular polygon with 6 sides = 720°
Interior Angle of Regular Polygon = (Sum of All Interior Angles) / (Number of Sides in Regular Polygon)
Interior angle of a regular polygon with 6 sides = 720°/6
Interior angle of a regular polygon with 6 sides = 120°
Example 5: Find the sum of interior angles of regular pentagon if the number of triangles formed in the regular pentagon is 3.
Solution:
Number of triangles formed in the regular pentagon = 3
Sum of Interior Angles of a Polygon = Number of Triangles Formed in Polygon × 180°
Sum of interior angles of regular pentagon = 3 × 180°
Sum of interior angles of regular pentagon = 540°
Interior Angles of a Polygon
Interior angles of a polygon are angles within a polygon made by two sides. The interior angles in a regular polygon are always equal. The sum of the interior angles of a polygon can be calculated by subtracting 2 from the number of sides of the polygon and multiplying by 180°. Sum of Interior Angles = (n − 2) × 180°
In this article, we will learn about the interior angles of a polygon, the sum of interior angles of a polygon, the formula for the interior angles, and others in detail.
Table of Content
- What is Angle?
- What are Interior Angles of Polygons?
- Sum of Interior Angles Formula
- Interior Angles Theorem
- Sum of Interior Angles of a Polygon
- Interior Angles in Different Types of Polygons
- Interior and Exterior Angles of a Polygon
- Exterior Angles
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