One angle

One angle is 10 degrees more than four times the measure of the other angle. Together they have a sum of 120 degrees. What is the measure of each angle?

Correct answer:

α =  98 °
β =  22 °

Step-by-step explanation:

$$\begin{gathered} \alpha =10+4\cdot \beta \\ \alpha +\beta =120 \\ \alpha -4\beta =10 \\ \alpha +\beta =120 \\ Row2-Row1\to Row2 \\ \alpha -4\beta =10 \\ 5\beta =110 \\ \beta =\frac{110}{5}=22 \\ \alpha =10+4\beta =10+4\cdot 22=98=98^{\circ } \\ \alpha =98 \\ \beta =22 \end{gathered}$$

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