Angles of a triangle

In triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle.

Correct answer:

α =  30 °
β =  45 °
γ =  105 °

Step-by-step explanation:

β=15+α γ=30+α+β α+β+γ=180  αβ=15 α+βγ=30 α+β+γ=180  Row2Row1Row2 αβ=15 2βγ=15 α+β+γ=180  Row3Row1Row3 αβ=15 2βγ=15 2β+γ=195  Row3Row2Row3 αβ=15 2βγ=15 2γ=210  γ=2210=105 β=215+γ=215+105=45 α=15+β=15+45=30=30  α=30 β=45 γ=105

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