## 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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