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Question Number 182546 by Acem last updated on 11/Dec/22

Commented by Acem last updated on 11/Dec/22

$$Modify:Findthegreatestandtheleastangles$$$$inrad.$$

Answered by Rasheed.Sindhi last updated on 11/Dec/22

$$Angles:a,a+d,a+2d,a+3d$$$$\bullet a+3d=2a\Rightarrow a=3d$$$$\bullet 3d+4d+5d+6d=2\pi \left(Sumofangles\right)$$$$18d=2\pi \Rightarrow d=\frac{\pi }{9}$$$$3\left(\frac{\pi }{9}\right),4\left(\frac{\pi }{9}\right),5\left(\frac{\pi }{9}\right),6\left(\frac{\pi }{9}\right)$$$$\frac{\pi }{3},\frac{4\pi }{9},\frac{5\pi }{9},\frac{2\pi }{3}$$

Commented by Acem last updated on 11/Dec/22

$$Ihaveaquestion:$$$$Itriedtoassunethattheanglesare:$$$$(x+3y)°,(x+y)°,(x-y)°,(x-3y)°$$$$andgotthesameyourangles$$$$$$$$Theniassumedthattheanglesare:$$$$(x+2y)°,(x+y)°,(x-y)°,(x-2y)°$$$$andgot:\frac{\pi }{3},\frac{7\pi }{12},\frac{15\pi }{36},\frac{2\pi }{3}$$$$why{aren}^{\prime }ttheythesame?$$$$$$

Commented by mr W last updated on 11/Dec/22

$$inway1thedifferencebetweenany$$$$twoconsecutivetermsis-2y.{that}^{\prime }s$$$$correct.$$$$inway2thedifferencebetweenthe$$$$firstandthesecondtermaswellas$$$$betweenthethirdandfourthterm$$$$is-y,but{it}^{\prime }s-2ybetweenthesecondand$$$$thethirdterm.thisisnotaA.P.!$$

Commented by Rasheed.Sindhi last updated on 11/Dec/22

$$\mathcal{T}hanksss\mathit{m}\mathit{r}\mathit{W}\mathit{s}\mathit{i}\mathit{r}!$$

Answered by manxsol last updated on 11/Dec/22

$$a+(a+r)+(a+2r)+(a+3r)=360$$$$a+3r=2a\Rightarrow a=3r$$$$angles3r+4r+5r+6r=2\pi$$$$18r=2\pi$$$$r=\frac{\pi }{9}$$$$greast\frac{2\pi }{3}$$$$least\frac{\pi }{3}$$$$$$$$$$

Commented by Acem last updated on 11/Dec/22

$$Thanksss!$$

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