Understanding Quadrilaterals - Maths Class 8th - Ex 3.2 - Q4 - Chapter 3 - NCERT - CBSE
Understanding Quadrilaterals - Maths Class 8th - Ex 3.2 - Question 4 - Chapter 3 - NCERT - CBSE
Full exercise on Understanding Quadrilaterals, fully solved. This is a video tutorial for 8th class NCERT CBSE students. For other educational stuff, subscribe and press bell icon.
Sum of the Measures of the Exterior Angles of a Polygon
On many occasions a knowledge of exterior angles may throw light on the nature of interior angles and sides. This is true whatever be the number of sides of the polygon. Therefore, the sum of the measures of the external angles of any polygon is 360 degrees.
Example 1: Find measure x in Fig 3.9.
Example 2: Find the number of sides of a regular polygon whose each exterior angle has a measure of 45°.
Introduction
You know that the paper is a model for a plane surface. When you join a number of points without lifting a pencil from the paper (and without retracing any portion of the drawing other than single points), you get a plane curve.
Polygons
A simple closed curve made up of only line segments is called a polygon.
Classification of polygons
We classify polygons according to the number of sides (or vertices) they have. Triangle,Quadrilateral,Pentagon,Hexagon,Heptagon,Octagon,Nonagon,Decagon and n-gon.
Diagonals
Adiagonalis a line segment connecting two non-consecutive vertices of a polygon.
Convex and concave polygons
Can you find how these types of polygons differ from one another? Polygons that are convex have no portions of their diagonals in their exteriors.
Regular and irregular polygons
A regular polygon is both ‘equiangular’and ‘equilateral’. For example, a square has sides of equal length and angles of equal measure. Hence it is a regular polygon. A rectangle is equiangular but not equilateral. Is a rectangle a regular polygon? Is an equilateral triangle a regular polygon? Why?
Angle sum property
Do you remember the angle-sum property of a triangle? The sum of the measures of the three angles of a triangle is 180°. Recall the methods by which we tried to visualise this fact. We now extend these ideas to a quadrilateral.
EXERCISE 3.2
1. 1. Find xin the following figures.
2. Find the measure of each exterior angle of a regular polygon of (i) 9 sides (ii) 15 sides
3. How many sides does a regular polygon have if the measure of an exterior angle is 24°?
4. How many sides does a regular polygon have if each of its interior angles is 165°?
5. (a) Is it possible to have a regular polygon with measure of each exterior angle as 22°? (b) Can it be an interior angle of a regular polygon? Why?
6. (a) What is the minimum interior angle possible for a regular polygon? Why? (b) What is the maximum exterior angle possible for a regular polygon?
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