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 50o?
Since 7.2 is not a whole number. So, it is not it possible to have a regular each of whose exterior angles is 50o.
(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 100o?
Solution: Each interior angles = 180o – (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 100o.
(5) What is the sum of all interior angles of a regular
(i) Pentagon = (10 – 4) right angles = 6 × 90 = 540o
(ii) Hexagon = (12 – 4) right angles = 8 × 90 = 720o
(iii) Nonagon = (18 – 4) right angles = 16 × 90 = 1440o
(iv) Polygon of 12 sides = (24 – 4) right angles = 20 × 90 = 1800o
(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 = 108o
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