Class 8 Maths Chapter 3 Understanding quadrilaterals exercise 3.2 pdf notes:-
Exercise 3.2 Class 8 maths Chapter 3 Pdf Notes:-
Ncert Solution for Class 8 Maths Chapter 3 Understanding quadrilaterals Exercise 3.2 Tips:
Sum of the Measures of the Exterior Angles of a
On many occasions a knowledge of exterior angles may throw light on the nature of
interior angles and sides.
Draw a polygon on the floor, using a piece of chalk.
(In the figure, a pentagon ABCDE is shown).
We want to know the total measure of angles, i.e,
m∠1 + m∠2 + m∠3 + m∠4 + m∠5. Start at A. Walk
along AB. On reaching B, you need to turn through an
angle of m∠1, to walk along BC . When you reach at C,
you need to turn through an angle of m∠2 to walk along
CD. You continue to move in this manner, until you return
to side AB. You would have in fact made one complete turn.
Therefore, m∠1 + m∠2 + m∠3 + m∠4 + m∠5 = 360°
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°.
Example 1: Find measure x in Fig 3.9.
Solution: x + 90° + 50° + 110° = 360° (Why?)
x + 250° = 360°
x = 110°
Take a regular hexagon
- What is the sum of the measures of its exterior angles x, y, z, p, q, r?
- Is x = y = z = p = q = r? Why?
- What is the measure of each?
(i) exterior angle (ii) interior angle
- Repeat this activity for the cases of
(i) a regular octagon (ii) a regular 20-gon
Example 2: Find the number of sides of a regular polygon whose each exterior angle
has a measure of 45°.
Solution: Total measure of all exterior angles = 360°
Measure of each exterior angle = 45°
Therefore, the number of exterior angles =
45 = 8
The polygon has 8 sides.