Can we find two other angles of a triangle if we have only one angle?

Question

Can we find two other angles of a triangle if we have only one angle? If yes, then how?

Answer 1

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.

Answer 2

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.