In a triangle abc , if 2 angle A = 3 angle B = 6 angle C , calculate the measures of angle A , angle B and angle C.
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2 /_ A = 3 /_ B = 6 /_ C
Let 2 /_ A = 3 /_ B = 6 /_ C = X° . Then,
/_ A = (X/2)° , /_B = (X/3)° and /_ C = (X/6)°
Therefore,
X/2 + X/3 + X/6 = 180
3X + 2X + X = 1080
6X = 1080
X = 180
Therefore,
/_ A = X/2 = 180°/2 = 90°
/_ B = X/3 = 180°/3 = 60°
And,
/_ C = X/6 = 180°/6 = 30°.
2 /_ A = 3 /_ B = 6 /_ C
Let 2 /_ A = 3 /_ B = 6 /_ C = X° . Then,
/_ A = (X/2)° , /_B = (X/3)° and /_ C = (X/6)°
Therefore,
X/2 + X/3 + X/6 = 180
3X + 2X + X = 1080
6X = 1080
X = 180
Therefore,
/_ A = X/2 = 180°/2 = 90°
/_ B = X/3 = 180°/3 = 60°
And,
/_ C = X/6 = 180°/6 = 30°.
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