A hexagon has interior angles in arithmetic progression where difference of angles is double the sma

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05 Apr 2022 Geometry

A hexagon has interior angles in arithmetic progression where difference of angles is double the smallest angle. The measure of largest interior angle of this hexagon is

OPtion

1) 240
2) 220
3) 185
4) 360
5) 440
6) 275
7) 110
8) 270
9) 330
10) None of these

Solution

Sum of interior angles of a polygon with 'n' sides = 180*(n-2)
.'. Sum of interior of of a hexagon = 180*(6-2) = 720°
Given, Internal angles are in A.P. Let the six angles be x, x+d, x+2d, x+3d, x+4d, x+5d
Also, the difference 'd' between angles is double the smallest angle ⇒ d=2x
.'. The angles are x, (x+2x), (x+4x), (x+6x), (x+8x), (x+10x) or x, 3x, 5x, 7x, 9x, 11x
Sum of interior angles = 36x = 720
⇒ x=20
Hence, largest angle = 11x = 220°

Correct Option: 2 Best Solution (4)

G.S.Kantharao   2 years AGO

Angles are in degrees =x,3x,5x,7x,9x,11x
Sum=36x°=720°=>x=20°
Largest is 11x°=11*20°=220°
My option is 2👈

Like? Yes (6) | No   

Varun   2 years AGO

The values are a, a+r, a+2r, ... a+5r
We also know sum of interior angles = 720
=> a+15r = 720
Given r = 2a
So a+15(2a) = 720
or a = 20
=> Largest = a+5r = 20+5(2*20) = 220

Like? Yes (2) | No   

Pargat Pal Singh   2 years AGO

let angles are x,3x,5x,7x,9x and 11x.
Sum of interior angles of hexagon= 180*(n-2)= 36x
x=720/36=20
largest angle=11x= 220

Like? Yes (2) | No (1)  

Mayank Kandoi   2 years AGO

Let the smallest angle be a. Then,
a2 = a + 2a = 3a
a3 = a + 4a = 5a
a4 = a + 6a = 7a
a5 = a + 8a = 9a
a6 = a + 10a = 11a

Sum of all angles = (6-2)*180 = 4*180
(1 + 3 + 5 + 7 + 9 + 11)a = 4*180
36a = 4*180
a = 20
Largest angle = 11a = 11*20 = 220

Option 2

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