Angles in a triangle

The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=100°.

What sizes have other angles in a triangle?

Final Answer:

α =  20 °
β =  60 °

Step-by-step explanation:

γ=100 ∘  α+β+γ = 180  ∘ β = α + d γ = α + 2d  3 α + 3d = 180  ∘ 2 α + d = 180 − γ = 80  ∘  d = 180−γ−2α  3⋅ α+3(180−γ−2⋅ α)=180 3⋅ α+3(180−100−2⋅ α)=180  3⋅ α+3⋅ (180−100−2⋅ α)=180  3α=60  α=360​=20=20∘  α=20  d=180−γ−2⋅ α=180−100−2⋅ 20=40 ∘
β=α+d=20+40=60=60∘   Verifying Solution:  s=α+β+γ=20+60+100=180 ∘  c=α+2⋅ d=20+2⋅ 40=100 ∘

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You need to know the following knowledge to solve this word math problem:

statisticsalgebraplanimetryUnits of physical quantitiesGrade of the word problem

 
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