Class 8 Maths Chapter 3 Understanding quadrilaterals exercise 3.2 pdf notes:-

**Exercise 3.2** Class 8 maths Chapter 3 Pdf Notes:-

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## Ncert Solution for Class 8 Maths Chapter 3 Understanding quadrilaterals Exercise 3.2 Tips:

**Sum of the Measures of the Exterior Angles of aPolygon**

On many occasions a knowledge of exterior angles may throw light on the nature of

interior angles and sides.

**TRY THESE**

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,

mā 1 + mā 2 + mā 3 + mā 4 + mā 5. Start at A. Walk

along AB. On reaching B, you need to turn through an

angle of mā 1, to walk along BC . When you reach at C,

you need to turn through an angle of mā 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, mā 1 + mā 2 + mā 3 + mā 4 + mā 5 = 360Ā°

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 360Ā°.

Example 1: Find measure x in Fig 3.9.

Solution: x + 90Ā° + 50Ā° + 110Ā° = 360Ā° (Why?)

x + 250Ā° = 360Ā°

x = 110Ā°

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 45Ā°.

Solution: Total measure of all exterior angles = 360Ā°

Measure of each exterior angle = 45Ā°

Therefore, the number of exterior angles =

360

45 = 8

The polygon has 8 sides.