Question

36. The ages of Arjun and Sahadev are in the ratio 4:5. After 5 years their ages will be in the ratio 5:6. (3) Find their present ages. 77 Find the measure of an exterior angle of a regular pentagon and the interior angle of a regular​

Answer 1

Answer:

36. Arjun is 20 years old and Sahadev is 25 years old.

77. Exterior angle is 72° and interior angle is 108°

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Step-by-step explanation:

Let age of Arjun 4x

Let age of Sahadev be 5x   [Since ratio of agess is 4:5]

(4x + 5)/(5x + 5) = 5/6           [Since after 5 years ratio is 5:6]

6(4x + 5) = 5(5x + 5)

24x + 30 = 25x + 25

30 - 25 = 25x - 24x

x = 5

4x = 20

5x = 25

Sum of exterior angles of any polygon = 360°

All exterior angles are equal regular pentagon

No. of exterior angles = 5

Measure of each exterior angle = 360°/5  = 72°

Sum of interior angles of a polygon

= 180°(n-2) or (180n)° - 360° (whichever is given in your tb)

Here, n = 5

= 180°(5-2)

= 540°

Number of interior angles in pentagon = 5

All interior angles are equal in regular pentagon

Measure of each angle = 540°/5

= 108°