RS Aggarwal Class 8 Math Fourteenth Chapter Polygons Exercise 14A Solution

EXERCISE 14A

(1) Find the measure of each exterior angle of a regular

(2) Is it possible to have a regular each of whose exterior angles is 50^o?

Since 7.2 is not a whole number. So, it is not it possible to have a regular each of whose exterior angles is 50^o.

(3) Find the measure of each interior angle of a regular polygon having

(i) 10 sides (ii) 15 sides

(4) Is it possible to have a regular polygon each of whose interior angles is 100^o?

Solution: Each interior angles = 180^o – (each exterior angle)

Let the exterior angle be x.

Since, 4.5 is not a whole number. So, it is not possible to have a regular polygon each of whose interior angles is 100^o.

(5) What is the sum of all interior angles of a regular

(i) Pentagon = (10 – 4) right angles = 6 × 90 = 540^o

(ii) Hexagon = (12 – 4) right angles = 8 × 90 = 720^o

(iii) Nonagon = (18 – 4) right angles = 16 × 90 = 1440^o

(iv) Polygon of 12 sides = (24 – 4) right angles = 20 × 90 = 1800^o

(6) What is the number of diagonals in a

(7) Find the number of sides of a regular polygon whose each exterior angle measures:

(8) In the given figure, find the angle measure x.

Solution: (90 + 50 + 115 + x) = 360

⇒ 255 + x = 360

⇒ x = 360 – 255 = 105

(9) Find the angle measure x in the given figure.

Solution: (2 × 5 – 4) right angles

= (10 – 4) right angles

= 6 × 90 = 540

∴ 5x = 540

⇒ x = 108^o

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