The correct option is C 680^o α=70^ o , #10;90^ o lt;β lt;180^ o , 180^ o lt;γ lt;270^ o , 270^ o #10; lt;δ lt;360^ o .Let d be th ...

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Sum of n Terms

If α+β+γ+δ=...

Question

If $α + β + γ + δ = θ$ and $α = 70^{o}$ , then

400^{o} < θ < 580^{o}

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470^{o} < θ < 650^{o}

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680^{o} < θ < 860^{o}

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540^{o} < θ < 900^{o}

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Solution

The correct option is C $680^{o} < θ < 860^{o}$
$α = 70^{o}, 90^{o} < β < 180^{o}, 180^{o} < γ < 270^{o}, 270^{o} < δ < 360^{o}$ .
Let d be the difference of the A.P.
Then, $β = α + d, γ = α + 2 d, δ = α + 3 d .$
$\Rightarrow β + γ + α + δ = 4 α + 6 d,$
$\Rightarrow 270^{o} < α + 3 d < 360^{o}$
$\Rightarrow 200^{o} < 3 d < 290^{o}$
$\Rightarrow 400^{o} < 6 d < 580^{o}$
$\Rightarrow 680^{o} < 4 α + 6 d < 860^{o}$
$\Rightarrow 680^{o} < θ < 860^{o}$

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