Angle Measure Of A Pentagon
In Geometry, a pentagon is a two-dimensional effigy having v sides and 5 angles. In a pentagon, an angle is formed when the two sides of the pentagon share a common point. Since the number of vertices in a pentagon is 5, the number of angles in a pentagon is five. In this article, nosotros are going to hash out the angles in a pentagon, such as interior angles, exterior angles, the sum of angles in a pentagon, etc., in detail with many examples.
Before discussing the angles in a pentagon, permit the states first discuss what a pentagon is? and different types of pentagons.
Pentagon and its Types
A pentagon is a closed two-dimensional polygon with 5 sides and 5 angles. Based on the properties, a pentagon tin exist classified into different 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 non 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 i of the interior angles of a pentagon is greater than 180° and if i of the vertices points in, then it is called a concave polygon.
The post-obit figure depicts the definition of a regular pentagon, irregular pentagon, and concave pentagon respectively.
Sum of Angles in a Pentagon
The sum of angles in a pentagon is the sum of five angles of the pentagon. Now let 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, and so the sum of angles in a pentagon = 3 × 180° = 540°.
Nosotros can also calculate the sum of interior angles of the pentagon in the following way:
Nosotros know that the sum of the interior angles of a polygon of n sides = (n – 2) × 180°.
Since a pentagon has 5 sides, the sum of interior angles of a pentagon is = (5-2)× 180° [where due north=five]
= 3× 180°= 540°.
Hence, the sum of interior angles of a pentagon is 540°.
Sum of Exterior 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.
We know that each exterior bending is supplementary to the interior bending.
Thus, from the higher up formula, nosotros tin derive each exterior angle = [180°due north -180°n + 360°]/n = 360°/n
Therefore, the sum of exterior angles of a polygon = n(360°/n).
As, the number of sides in a pentagon is five, due north=5.
Thus, the sum of exterior angles of a pentagon = five(360°/5) = 360°.
Interior Angle of a Regular Pentagon
The angles formed by two adjacent pairs of sides are called interior angles of a pentagon.
Number of sides = Number of vertices = Number of interior angles = v
Two interior angles that share a mutual side are called adjacent angles or side by side interior angles.
A regular pentagon has all its five sides equal and all five angles are also equal. Hence, the measure out of each interior angle of a regular pentagon is given by the below formula.
Measure of each interior bending = [(north – 2) × 180°]/n = 540°/v = 108°.
Here, n = Number of sides
Read more:-
- Types Of Polygon
- Area Of Polygon
- Perimeter Of Polygons
- Congruence Of Triangles Class nine
Outside 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 bending of a pentagon is equal to 72°.
Since the sum of exterior angles of a regular pentagon is equal to 360°, the formula to summate each exterior bending of a regular pentagon is given as follows:
The measure of each exterior angle of a pentagon = 360°/n = 360°/5 = 72°.
Central Bending of a Pentagon
The measure of the key bending of a regular pentagon makes a circle, i.e. total measure out is 360°. If we split the pentagon into five coinciding triangles, so the angle at one vertex of them will be 72° (360°/v = 72°).
Angles in a Pentagon Examples
Example 1:
Three angles of a pentagon are lxxx°, 70° and 100°, so the other ii angles can exist 145° and 145° or 120° and 180°?
Solution:
Given 3 angles are eighty°, 70° and 100°.
Sum of 3 angles = 80° + 70° + 100° = 250°
We know that the sum of all the five angles of a pentagon is 540°.
Sum of the other two angles = 540° – 250° = 290°
Now,
145° + 145° = 290°
120° + 180° = 300°
Hence, the other two angles of a pentagon are 145° and 145°.
Instance 2:
Find the value of 10 from the beneath-given figure of the pentagon.
Solution:
Given that, one of the angles of a pentagon is a right angle, i.e. 90°.
By bending sum holding of a pentagon,
x + xc° + 115° + 125° + 106° = 540°
10 + 436° = 540°
ten = 540° – 436°
x = 104°
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Frequently Asked Questions on Angles in a Pentagon
What is the measure of each interior angle of a regular pentagon?
The measure of each interior angle of a regular pentagon is 108°
What is the mensurate of each exterior angle of a regular pentagon?
The measurement of each exterior angle 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 bending of a regular pentagon is 72°.
Angle Measure Of A Pentagon,
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