Pls answer 3b and challenge with full working out
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Answer:
Step-by-step explanation:
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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, °
⇒ °
⇒
⇒
⇒ °
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.