AB ,BC , CD are the three consecutive sides of a regular polygon If angle - Maths -

Question

AB ,BC , CD are the three consecutive sides of a regular
polygon
If angle BAC =20 degree , find :-
1) one exterior angle
2) no of sides of the polygon

Lalit Mehra · Accepted Answer

Let the number of sides of the regular polygon be n.

Given: AB, BC, CD are three consecutive sides of the regular polygon and ∠BAC = 20°.

In ΔABC,

AB = BC (Sides of regular polygon are equal)

∴ ∠BCA = ∠BAC (Equal sides have equal angles opposite to them)

⇒ ∠BCA = ∠BAC = 20°

∠BCA + ∠ABC + ∠BAC = 180°

∴ 20° + ∠ABC + 20° = 180°

⇒ ∠ABC = 180° – 40° = 140°

Each interior angle of the given regular polygon is 140°.

We know that, each interior angle of the regular polygon $= \frac{(n - 2) \times 180 °}{n}$ .

$∴ \frac{(n - 2) \times 180 °}{n} = 140 ° \Rightarrow 9 n - 18 = 7 n \Rightarrow 9 n - 7 n = 18 \Rightarrow 2 n = 18 \Rightarrow n = 9$

Number of sides of the regular polygon = 9

Sum of all exterior angles of the polygon is 360°.

∴ Each exterior angle of the regular polygon $= \frac{360 °}{9} = 45 °$

35

AB ,BC , CD are the three consecutive sides of a regular polygon . If angle BAC =20 degree , find :- 1) one exterior angle .2) no of sides of the polygon .

AB ,BC , CD are the three consecutive sides of a regular polygon .

If angle BAC =20 degree , find :-

1) one exterior angle .
2) no of sides of the polygon .