Hello friends we are back again with another new session. In our today’s session we will discuss angles. Many students find geometry a difficult topic but after today’s session you will find it interesting and easy to deal with.
Today we will discuss Angles of Triangles and Polygons.
A grade XI student is aware that triangle is a type of polygon. As polygon means many sides and triangle is a three side polygon. (Do you want to know What are Adjacent Angles)
Now let’s start with the Angles of Triangles and Polygons. Here we will include triangle in polygons and discuss it inside a polygon.
A triangle has interior and exterior angles. As a grade XI student I think you all know what are interior and exterior angles and what is the difference between them?
The sum of all three interior is 180 degree and sum of interior and exterior angles meets at one point is also 180 degree.
For a polygon the sum of polygon with n sides has interior angle 180 * (n-2). Suppose we have pentagon that is a polygon of 5 sides. Here we have 1, 2, 3, 4, 5 interior angles and 6, 7, 8, 9, 10 exterior angles.
Then the sum of interior angles are 180 * (5-2) = 540. As we know sum of angles meets at one point is 180 degree. From this we can calculate sum of all angles.
Angle 1 + Angle 6 + Angle 2 + Angle 7 + Angle 3 + Angle 8 + Angle 4 + Angle 9 + Angle 5 + Angle 10 = 5*(180) = 900
Now we can calculate sum of exterior angles from the above two calculations.
Exterior angles = sum of all – interior angles
= 900 – 540
= 360
Angle 1 + Angle 2 + Angle 3 + Angle 4+ Angle 5 (All interior angle) = 540
Angle 6 + Angle 7 + Angle 8 + Angle 8+ Angle 10 (All exterior angle) = 360
There are three types of angles.
What is an Acute Angle? Angle which is less than 90 degree and any triangle which has acute angle is called acute angle triangle.
Right Angle: An angle of 90 degree is called right angle and which has acute angle is called right angle triangle.
Obtuse Angle: Angle which is larger than 90 degree and any triangle which has acute angle is called obtuse angle triangle.
Now let’s see some polygons and their angles.
Square or Quadrilaterals:has 4 sides and its interior angle has 360 degree. Because a square has two triangles in it. Didn’t you notice this!
Pentagon:has 5 sides. A pentagon has 3 triangles inside it so the sum of interior angles are 3*180 = 540.
It is not possible to explain all polygons. So here is the list of some polygons with number of sides they have their interior angle.
If we want to compute the size of each angle then we can use
(n-2) * 180 / n, where n is the number of sides.
Example: For triangle each angle is
(3-2) * 180/ 3 = 60 degrees
In upcoming posts we will discuss about Trigonometric Ratios in grade XI and Special right triangles. Visit our website for information on ICSE board syllabus for class 12 math
Today we will discuss Angles of Triangles and Polygons.
A grade XI student is aware that triangle is a type of polygon. As polygon means many sides and triangle is a three side polygon. (Do you want to know What are Adjacent Angles)
Now let’s start with the Angles of Triangles and Polygons. Here we will include triangle in polygons and discuss it inside a polygon.
A triangle has interior and exterior angles. As a grade XI student I think you all know what are interior and exterior angles and what is the difference between them?
The sum of all three interior is 180 degree and sum of interior and exterior angles meets at one point is also 180 degree.
For a polygon the sum of polygon with n sides has interior angle 180 * (n-2). Suppose we have pentagon that is a polygon of 5 sides. Here we have 1, 2, 3, 4, 5 interior angles and 6, 7, 8, 9, 10 exterior angles.
Then the sum of interior angles are 180 * (5-2) = 540. As we know sum of angles meets at one point is 180 degree. From this we can calculate sum of all angles.
Angle 1 + Angle 6 + Angle 2 + Angle 7 + Angle 3 + Angle 8 + Angle 4 + Angle 9 + Angle 5 + Angle 10 = 5*(180) = 900
Now we can calculate sum of exterior angles from the above two calculations.
Exterior angles = sum of all – interior angles
= 900 – 540
= 360
Angle 1 + Angle 2 + Angle 3 + Angle 4+ Angle 5 (All interior angle) = 540
Angle 6 + Angle 7 + Angle 8 + Angle 8+ Angle 10 (All exterior angle) = 360
There are three types of angles.
What is an Acute Angle? Angle which is less than 90 degree and any triangle which has acute angle is called acute angle triangle.
Right Angle: An angle of 90 degree is called right angle and which has acute angle is called right angle triangle.
Obtuse Angle: Angle which is larger than 90 degree and any triangle which has acute angle is called obtuse angle triangle.
Now let’s see some polygons and their angles.
Square or Quadrilaterals:has 4 sides and its interior angle has 360 degree. Because a square has two triangles in it. Didn’t you notice this!
Pentagon:has 5 sides. A pentagon has 3 triangles inside it so the sum of interior angles are 3*180 = 540.
It is not possible to explain all polygons. So here is the list of some polygons with number of sides they have their interior angle.
| Polygon | Sides | Sum of interior angles |
| Triangle | 3 | 180 |
| Quadrilateral | 4 | 360 |
| Pentagon | 5 | 540 |
| Hexagon | 6 | 720 |
| Heptagon | 7 | 900 |
| Octagon | 8 | 1082 |
If we want to compute the size of each angle then we can use
(n-2) * 180 / n, where n is the number of sides.
Example: For triangle each angle is
(3-2) * 180/ 3 = 60 degrees
In upcoming posts we will discuss about Trigonometric Ratios in grade XI and Special right triangles. Visit our website for information on ICSE board syllabus for class 12 math
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