Can I find other angles of triangle If I have only 1 angle?

Question

The problems goes like: "In a triangle there is inside angle B(beta) by 10 bigger than angle A(alpha). And agle Y(gamma) is 3 times bigger than angle B(beta). Define all angles." It's not stated what kind of Triangle it is, nothing. So is it even possible to do it?

You can write it I think like: A = B +10 , Y = B x 3 Still no idea.

Answer 1

From your question, I have: $$\left\{\begin{matrix} \alpha+\beta+\gamma=180° \\ \alpha=\beta+10° \\ \gamma=3\beta \end{matrix}\right.$$And then: $$\left\{\begin{matrix} 5\beta=170° \\ \alpha=\beta+10° \\ \gamma=3\beta \end{matrix}\right.$$ So the solutions are: $$\left\{\begin{matrix} \gamma=102° \\ \alpha=44° \\ \beta=34° \end{matrix}\right.$$

Answer 2

Working in degrees,

$\beta = \alpha +10$

$\gamma =3\beta = 3\alpha + 30$

By angle sum of triangle, $\alpha +\beta +\gamma = 180$

So $5\alpha +40 =180$

$\alpha = 28,\beta = 38,\gamma = 114$