3. In a triangle $ABC$, it is given that $|AB|=|AC|$. If $\alpha+\gamma=117^{\circ}$, calculate the measures of all the interior angles of this triangle.
3. If in triangle $A B C$ it holds that $|A B|=|A C|$, then the triangle is isosceles with base $\overline{B C}$. 1 POINT

The angles at the base of the isosceles triangle are of equal size, so $\beta=\gamma$. $\quad 1$ POINT

From $\alpha+\gamma=117^{\circ}$ and $\alpha+\beta+\gamma=180^{\circ}$ it follows that $\beta=63^{\circ}$. 2 POINTS

Then $\gamma=63^{\circ} \quad 1$ POINT

and $\alpha=117^{\circ}-63^{\circ}=54^{\circ}$. 1 POINT

TOTAL 6 POINTS