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 ∘

Try another example


Did you find an error or inaccuracy? Feel free to send us. Thank you!







Tips for related online calculators
Looking for help with calculating arithmetic mean?
Looking for a statistical calculator?
Do you have a linear equation or system of equations and are looking for its solution? Or do you have a quadratic equation?
See also our trigonometric triangle calculator.

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

statisticsalgebraplanimetricsUnits of physical quantitiesGrade of the word problem

 
We encourage you to watch this tutorial video on this math problem: video1

Related math problems and questions: