Interior 39791

For the interior angles of a triangle, the angle β is twice as large, and the angle γ is three times larger than the angle α. Is this triangle right?

Result

x=

Yes

No

Step-by-step explanation:

$$\begin{gathered} B=2\cdot A \\ C=3\cdot A \\ A+B+C=180 \\ 2A-B=0 \\ 3A-C=0 \\ A+B+C=180 \\ Pivot:Row1\leftrightarrow Row2 \\ 3A-C=0 \\ 2A-B=0 \\ A+B+C=180 \\ Row2-\frac{2}{3}\cdot Row1\to Row2 \\ 3A-C=0 \\ -B+0.667C=0 \\ A+B+C=180 \\ Row3-\frac{1}{3}\cdot Row1\to Row3 \\ 3A-C=0 \\ -B+0.667C=0 \\ B+1.333C=180 \\ Row3+Row2\to Row3 \\ 3A-C=0 \\ -B+0.667C=0 \\ 2C=180 \\ C=\frac{180}{2}=90 \\ B=\frac{0-0.66666666666667C}{-1}=\frac{0-0.66666667\cdot 90}{-1}=60 \\ A=\frac{0+C}{3}=\frac{0+90}{3}=30 \\ A=30 \\ B=60 \\ C=90 \\ x=1 \end{gathered}$$

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