# 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 result:

α =  37 °
β =  60 °

#### Solution:

$\beta =\left(\alpha +\gamma \right)\mathrm{/}2=6{0}^{\circ }$

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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