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

Row 2 - Row 1 → Row 2
a+b+c = 180
-2b-c+d = -180
a-c+2d = 0
c = 83

Row 3 - Row 1 → Row 3
a+b+c = 180
-2b-c+d = -180
-b-2c+2d = -180
c = 83

Row 3 - -1/-2 · Row 2 → Row 3
a+b+c = 180
-2b-c+d = -180
-1.5c+1.5d = -90
c = 83

Row 4 - 1/-1.5 · Row 3 → Row 4
a+b+c = 180
-2b-c+d = -180
-1.5c+1.5d = -90
d = 23


d = 23/1 = 23
c = -90-1.5d/-1.5 = -90-1.5 · 23/-1.5 = 83
b = -180+c-d/-2 = -180+83-23/-2 = 60
a = 180-b-c = 180-60-83 = 37

a = 37
b = 60
c = 83
d = 23

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