Can we find two other angles of a triangle if we have only one angle? If yes, then how?
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4If 1 angle is the only known thing, then no. – infinitezero Jul 22 '19 at 10:39
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With $60º$, you can make a 60-60-60 triangle, or a 60-90-30 triangle, or a 60-59-61 triangle. There are many more counterexamples with different angles. – Toby Mak Jul 22 '19 at 10:44
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1By the way, there is absolutely no research effort in this question. – Toby Mak Jul 22 '19 at 10:47
2 Answers
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The sum of all angles of a triangle is constant. On a plane of curvature of zero (a Euclidian plane or flat plane), this is equal to 180 degrees. ie. $$180^{\circ} = \theta_1 + \theta_2 + \theta_3$$
In your case you know $\theta_1$ but $\theta_2$ and $\theta_3$ are unknown. This results in one equation with two unknowns.
Thus when one angle is given there is more information needed to find the other two angles.
ElderNoSpace
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If two triangles are similar, they have the same angles. The criteria needed for similarity of the other triangle are:
$$\text{AA or AAA (at least $2$ angles known)}$$ $$\text{SSS (all $3$ sides known)}$$ $$\text{SAS ($2$ sides and the angle in between is known)}$$
Since one angle known is not in the criteria needed for similarity, you cannot find the two other angles. As ElderNoSpace wrote, you need at least $1$ other angle to find these angles.
Toby Mak
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