The angles 5

The angles of a triangle are in arithmetic progression (AP). The greatest angle is twice the least. Find all the angles.

Correct answer:

α =  40 °
β =  60 °
γ =  80 °

Step-by-step explanation:

α+β+γ=180  ∘ γ = 2α AP: β−α  = γ−β = diff AP: β = (α+γ)/2  α+β+2α=180 α+(α+γ)/2+2α=180  α+(α+2α)/2+2α=180  3α+(3α)/2=180 6α+3α=360 9α=360  α=360/9=40=40∘  γ=2⋅ α=2⋅ 40=80 ∘
β=2α+γ​=240+80​=60=60∘  Verifying Solution:  s=α+β+γ=40+60+80=180 ∘

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