What Angle Is A Pentagon

In Geometry, a pentagon is a two-dimensional figure having 5 sides and 5 angles. In a pentagon, an bending is formed when the two sides of the pentagon share a mutual point. Since the number of vertices in a pentagon is five, the number of angles in a pentagon is 5. In this article, nosotros are going to discuss the angles in a pentagon, such every bit interior angles, exterior angles, the sum of angles in a pentagon, etc., in detail with many examples.

Earlier discussing the angles in a pentagon, let us beginning discuss what a pentagon is? and dissimilar types of pentagons.

Pentagon and its Types

A pentagon is a closed two-dimensional polygon with five sides and 5 angles. Based on the backdrop, a pentagon can be classified into unlike types. They are:

Regular Pentagon: A pentagon having all its sides and interior angles equal.

Irregular Pentagon: All the sides of a pentagon are not equal and the interior angles are not of the same measurement.

Convex Pentagon: All the interior angles are less than 180° and all the vertices point outwards. A regular pentagon is a convex pentagon.

Concave Pentagon: If one of the interior angles of a pentagon is greater than 180° and if one of the vertices points inward, then it is called a concave polygon.

The following effigy depicts the definition of a regular pentagon, irregular pentagon, and concave pentagon respectively.

Pentagon Shapes

Sum of Angles in a Pentagon

The sum of angles in a pentagon is the sum of 5 angles of the pentagon. At present allow us discuss the sum of interior and exterior angles of a pentagon.

Sum of Interior Angles in a Pentagon

Pentagon is formed from three triangles, so the sum of angles in a pentagon = 3 × 180° = 540°.

We can also calculate the sum of interior angles of the pentagon in the following style:

Nosotros know that the sum of the interior angles of a polygon of northward sides = (northward – 2) × 180°.

Since a pentagon has 5 sides, the sum of interior angles of a pentagon is = (5-2)× 180° [where n=5]

= 3× 180°= 540°.

Hence, the sum of interior angles of a pentagon is 540°.

Sum of Outside Angles in a Pentagon

We know that the formula to calculate the sum of interior angles of a polygon is (n – 2) × 180°.

Hence, each interior angle = [(n – ii) × 180°]/n.

Nosotros know that each outside bending is supplementary to the interior angle.

Thus, from the in a higher place formula, we can derive each outside angle = [180°n -180°n + 360°]/due north = 360°/n

Therefore, the sum of outside angles of a polygon = due north(360°/due north).

As, the number of sides in a pentagon is five, northward=five.

Thus, the sum of exterior angles of a pentagon = 5(360°/v) = 360°.

Interior Bending of a Regular Pentagon

The angles formed past two adjacent pairs of sides are called interior angles of a pentagon.

Number of sides = Number of vertices = Number of interior angles = 5

Two interior angles that share a common side are called adjacent angles or adjacent interior angles.

Interior Angles of a Pentagon

A regular pentagon has all its five sides equal and all five angles are also equal. Hence, the measure out of each interior bending of a regular pentagon is given past the below formula.

Measure of each interior angle = [(n – 2) × 180°]/n = 540°/5 = 108°.

Here, n = Number of sides

Angles in a Regular Pentagon

Read more than:-

Types Of Polygon
Area Of Polygon
Perimeter Of Polygons
Congruence Of Triangles Course ix

Exterior Angle of a Regular Pentagon

Exterior angles of a pentagon are the angles formed outside the pentagon with its sides when the sides of the pentagon are extended. Each outside angle of a pentagon is equal to 72°.

Since the sum of outside angles of a regular pentagon is equal to 360°, the formula to calculate each exterior angle of a regular pentagon is given as follows:

The mensurate of each outside angle of a pentagon = 360°/n = 360°/5 = 72°.

Interior and Exterior Angles of a Pentagon

Central Angle of a Pentagon

The mensurate of the key angle of a regular pentagon makes a circle, i.e. total measure is 360°. If we divide the pentagon into five congruent triangles, then the angle at one vertex of them will be 72° (360°/5 = 72°).

Central Angle of Regular Pentagon

Angles in a Pentagon Examples

Example 1:

Three angles of a pentagon are fourscore°, 70° and 100°, so the other two angles can be 145° and 145° or 120° and 180°?

Solution:

Given three angles are 80°, 70° and 100°.

Sum of three angles = 80° + 70° + 100° = 250°

We know that the sum of all the five angles of a pentagon is 540°.

Sum of the other ii angles = 540° – 250° = 290°

Now,

145° + 145° = 290°

120° + 180° = 300°

Hence, the other two angles of a pentagon are 145° and 145°.

Example ii:

Notice the value of x from the below-given effigy of the pentagon.

Angles in a Regular Pentagon Example

Solution:

Given that, one of the angles of a pentagon is a right angle, i.e. 90°.

By angle sum holding of a pentagon,

x + 90° + 115° + 125° + 106° = 540°

x + 436° = 540°

10 = 540° – 436°

ten = 104°

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Frequently Asked Questions on Angles in a Pentagon

What is the measure of each interior bending of a regular pentagon?

The measure of each interior angle of a regular pentagon is 108°

What is the measure of each outside angle of a regular pentagon?

The measurement of each exterior bending of a regular pentagon is 72°.

What is the sum of interior angles of a pentagon?

The sum of interior angles of a pentagon is 540°.

What is the sum of exterior angles of a pentagon?

The sum of exterior angles of a pentagon is 360°.

What is the measurement of the central angle of a regular pentagon?

The measurement of the central angle of a regular pentagon is 72°.