# 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:

$\alpha+\beta+\gamma = 180 \ \\ \beta = \alpha + d \ \\ \gamma = 83 ^\circ = \alpha + 2d \ \\ \ \\ 3 \alpha + 3d = 180 \ \\ 2 \alpha + d = 180 - \gamma = 23 ^\circ \ \\ \ \\ 3 \alpha + 3d = 180 \ \\ 2 \alpha + 2d = 23 \ \\ \ \\ \alpha = 37 ^\circ$
$\beta = (\alpha + \gamma)/2 = 60 ^\circ$

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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