Angles in a triangle

The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°.

What sizes have other angles in a triangle?

Correct answer:

α =  37 °
β =  60 °

Step-by-step explanation:

α+β+γ=180 β=α+d γ=83=α+2d  3α+3d=180 2α+d=180γ=23  3α+3d=180 2α+2d=23  α=37
β=(α+γ)/2=60

a+b+c = 180;b = a + d; c = a + 2d;c = 83

a+b+c = 180
b = a + d
c = a + 2•d
c = 83

a+b+c = 180
a-b+d = 0
a-c+2d = 0
c = 83

a = 37
b = 60
d = 23

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