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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.

Samčo Kaprális
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    Your other relation between the angles is that the angles in a triangle have to sum to a particular number. – Andrew Chin Mar 09 '20 at 16:02
  • Please clarify your question. Which is bigger, alpha or beta? – Deepak Mar 09 '20 at 16:10
  • Does this:"angle B(beta) by 10 bigger than angle A(alpha)" mean alpha is bigger? Or beta is bigger? – Deepak Mar 09 '20 at 16:15
  • Lets say it like that (really hard to translate). Beta is by 10 degrees bigger than Alpha. Does it help? so if you have Beta = x degress, and Alpha = Beta + 10 degrees. – Samčo Kaprális Mar 09 '20 at 17:06
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    @SamčoKaprális $30$ is ten more than $20$. That is to say, $30 = 20+10$, not $20=30+10$. So... "Beta is 10 degrees bigger than Alpha." That would be saying that $B = A+10$, not the other way around... so, again we ask... which is intended? Beta is 10 more than Alpha, in other words $B = A+10$? Or Alpha is 10 more than Beta, in other words $A = B+10$? Your most recent comment attempting to clarify mixed the two possibilities. – JMoravitz Mar 09 '20 at 18:38

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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: $$\left\{\begin{matrix} \gamma=102° \\ \alpha=44° \\ \beta=34° \end{matrix}\right.$$

Matteo
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Working in degrees,

$\beta = \alpha +10$

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

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

So $5\alpha +40 =180$

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

Deepak
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  • You don't have $\alpha=\beta+10$ – Matteo Mar 09 '20 at 16:10
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    @Matteo The phrasing of the question is ambiguous (written in bad English). But going by the most likely interpretation of the meaning, he got the relationship between alpha and beta reversed, as did you. Better await a clarification. – Deepak Mar 09 '20 at 16:13