Question

3. Find the number of sides of a regular polygon, when
each of its interior angles has a measure of:
(i) 135°
(ii) 120°
(iii) 170°
(iv) 168°
(v) 175°​

Answer 1

Answer:

10 sides

Step-by-step explanation:

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Answer 2

Answer:

1) 8 sides

Let's start with the assumption that the number of sides be n, this means that we have n sided regular polygon whose interior angle is 135∘. Therefore, we get the number of sides that the polygon has as 8.

2) 6 sides

if each interior angle is 120 then each exterior angle will 60. As we know that sum of exterior angle of polygon =360, side =360/60=6 . the number of sides=6.

3) 36 sides

A regular polygon with each interior angle of 170 deg will have each exterior angle as 180–170 = 10 deg. Hence the number of sides in the regular polygon = 360/10 = 36 sides.

4) 30 sides

The only number that stays the same for the angles of all polygons is that the sum of the exterior angles is 360°.

If you know the size of an exterior angle

(θ) in a regular polygon you can find the number of sides:

360°÷θ= number of sides

If you know the number of sides

(n) you can find the size of each exterior angle of a regular polygon.

360÷n=θ

Interior angle =168°

→exterior angle=

180°−168°=12°

360÷12°=30 sides.

5) 72 sides

A regular polygon with each interior angle of 175 deg will have each exterior angle as 180–175 = 5 deg. Hence the number of sides in the regular polygon = 360/5 = 72 sides.

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