Math, asked by WASAY139, 4 months ago

Pls answer 3b and challenge with full working out

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Answered by hinapakistani
3

Answer:

Step-by-step explanation:

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Answered by AadityaSingh01
1

Step-by-step explanation:

3b (i) The sum of interior angle and exterior angle of a regular polygon is 180°

so, exterior angle = 180° - 160° = 20°

(ii) If the interior angle of a regular polygon is 160 degrees, then the exterior angle is 20 degrees. The sum of all exterior angles is 360 degrees so there must be 360/20 sides = 18 sides.

(iii) The sum of the angles of a polygon is given by the formula:

(n-2)(180)

where n is the number of sides, which in this case is 18.

So we will replace n with 18 and evaluate.

(18-2)(180) = (16)(180) = 2880°

Challenge:- we know that sum of all angles of quadrilateral is 360°.

now, 2x + x + 20 + 2x - 10 + 3x + 30 = 180°

   ⇒ 8x + 40 = 180°

   ⇒ 8x = 180 - 40

   ⇒ x = \frac{140}{8}

   ⇒ x = 17.5°

now, 1st angle = 2 × 17.5 = 35°

2nd angle = 17.5 + 20 = 37.5°

3rd angle = 2 ×17.5 - 10 = 35 - 10 = 25°

4th angle = 3 × 17.5 + 30 = 35 + 30 = 65°

and, Smallest angle = 2x - 10 = 25°

hope it will help you.

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