# a) Find x + y + z

b) Find x + y + z + w

**Solution:**

The unknown angles can be estimated by using the angle sum property of a quadrilateral and triangle accordingly.

(a)

Sum of linear pair of angles is = 180°

x + 90° = 180° (Linear pair)

x = 180° - 90°

x = 90°

Solving for z

z + 30° = 180° (Linear pair)

z = 180° - 30°

z = 150°

Solving for y

y = 90° + 30° (Exterior angle theorem)

y = 120°

x + y + z = 90° + 120° + 150°

= 360°

(b)

The sum of the measures of all the interior angles of a quadrilateral is 360°. Using the angle sum property of a quadrilateral,

Let n be the fourth interior angle of the quadrilateral.

60° + 80° + 120° + n = 360°

260° + n = 360°

n = 360° - 260°

n = 100°

Sum of linear pair of angles is 180°

w + 100° = 180° ------- 1

x + 120° = 180° ------- 2

y + 80° = 180° ------- 3

z + 60° = 180° ------- 4

Adding equation (1), (2), (3) and (4),

w + 100° + x + 120° + y + 80° + z + 60° = 180° + 180° + 180° + 180°

w + x + y + z + 360° = 720°

w + x + y + z = 720° - 360°

w + x + y + z = 360°

Thus, the sum of the measures of the external angles of any polygon is 360°.

**☛ Check: **Class 8 Maths NCERT Solutions Chapter 3

**Video Solution:**

## a) Find x + y + z b) Find x + y + z + w

NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.1 Question 7

**Summary:**

(a) The value of x + y + z = 360° (b) The value of x + y + z + w = 360°

**☛ Related Questions:**

- What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try!)
- Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.) What can you say about the angle sum of a convex polygon with number of sides? (a) 7 (b) 8 (c) 10 (d) n
- What is a regular polygon? State the name of a regular polygon of (i) 3 sides (ii) 4 sides (iii) 6 sides
- Find the angle measure x in the following figures:

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