Find the angle measure x in the following figures:

Solution:

(a) The given figure has 4 sides and hence it is a quadrilateral

Using the angle sum property of a quadrilateral,

50° + 130° + 120° + x = 360°

300° + x = 360°

x = 360° -  300°

x = 60°

(b) Using the angle sum property of a quadrilateral.

The line is perpendicular to the base line hence, the angle formed is 90°.

90° + 60° + 70° + x = 360°

220° + x = 360°

220° + x = 360°

x = 360° - 220°

x = 140°

(c) The given figure is a pentagon (number of sides =5)

Angle sum of a polygon = (n - 2) × 180°

= (5 - 2) × 180°

= 3 × 180°

= 540°

Sum of the interior angle of pentagon is 540°.

Angles at the bottom are linear pairs.

Thus, First base interior angle,

= 180° - 70° (angle of straight line is 180° )

= 110°

Also, Second base interior angle,

= 180° - 60°

= 120°

Angle sum property of a polygon = (n - 2) × 180°

⇒ 30° + x + 110° + 120° + x = 540°

⇒ 2x + 260° = 540°

⇒ 2x = 540° - 260°

⇒ 2x = 280°

⇒ x = 280°/2

Therefore, x = 140°

(d) The given figure is pentagon (number of sides =5)

Sum of the interior angle of pentagon is 540°

Angle sum of a polygon

= (n - 2) × 180°

= (5 - 2) × 180°

= 3 × 180°

= 540°

Let each angle of the polygon be x since it is a regular pentagon.

Angle sum of a polygon = x + x + x + x + x = 540°

5x = 540°

x = 540°/5

x = 108°

The given pentagon is a regular polygon i.e. it is both ‘equilateral’ and ‘equiangular’. Thus, the measure of each interior angle of the pentagon is equal.

Hence each interior angle is 108°

☛ Check: NCERT Solutions for Class 8 Maths Chapter 3

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Video Solution:

Find the angle measure x in the following figures:
 

NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.1 Question 6

Summary:

The angle measure of x in the following figures are: (a) 60° (b) 140° (c) 140° (d) 108°.

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☛ Related Questions:

• How many diagonals does each of the following have? (a) A convex quadrilateral (b) A regular hexagon (c) A triangle
• 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