Triangle 5851

In a triangle, the first angle is half the second angle, and the third angle is the third of the first angle. How big are the angles in a triangle, and what is the type of triangle?

Correct answer:

A =  54 °
B =  108 °
C =  18 °

Step-by-step explanation:

$$\begin{gathered} A=\frac{B}{2} \\ C=\frac{A}{3} \\ A+B+C=180 \\ A=B/2 \\ C=A/3 \\ A+B+C=180 \\ 2A-B=0 \\ A-3C=0 \\ A+B+C=180 \\ Row2-\frac{1}{2}\cdot Row1\to Row2 \\ 2A-B=0 \\ 0.5B-3C=0 \\ A+B+C=180 \\ Row3-\frac{1}{2}\cdot Row1\to Row3 \\ 2A-B=0 \\ 0.5B-3C=0 \\ 1.5B+C=180 \\ Pivot:Row2\leftrightarrow Row3 \\ 2A-B=0 \\ 1.5B+C=180 \\ 0.5B-3C=0 \\ Row3-\frac{0.5}{1.5}\cdot Row2\to Row3 \\ 2A-B=0 \\ 1.5B+C=180 \\ -3.333C=-60 \\ C=\frac{-60}{-3.33333333}=18 \\ B=\frac{180-C}{1.5}=\frac{180-18}{1.5}=108 \\ A=\frac{0+B}{2}=\frac{0+108}{2}=54 \\ A=54 \\ B=108 \\ C=18 \end{gathered}$$

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