Triangle angles

In a triangle, ABC, the interior angle at vertex C is twice the internal angle at point A. The outer angle at point B measured 117 degrees. How big is the external angle at vertex A?

Correct answer:

a =  39 °

Step-by-step explanation:


a+b+c=180
c = 2a
180-b = 117

a+b+c=180
c = 2·a
180-b = 117

a+b+c = 180
2a-c = 0
b = 63

Pivot: Row 1 ↔ Row 2
2a-c = 0
a+b+c = 180
b = 63

Row 2 - 1/2 · Row 1 → Row 2
2a-c = 0
b+1.5c = 180
b = 63

Row 3 - Row 2 → Row 3
2a-c = 0
b+1.5c = 180
-1.5c = -117


c = -117/-1.5 = 78
b = 180-1.5c = 180-1.5 · 78 = 63
a = 0+c/2 = 0+78/2 = 39

a = 39
b = 63
c = 78

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