10. If triangle $\mathrm{ABC}$ has an interior angle of 30 degrees, and it can be divided into two isosceles obtuse triangles, then the other two interior angles are degrees. (Please write down all possible cases)
【Answer】 $15^{\circ}, 135^{\circ}$ or $10^{\circ}, 140^{\circ}$
【Analysis】Angle problem: The division of an isosceles triangle can be classified according to whether the 30-degree interior angle is divided. If the 30-degree interior angle is not divided, as shown in the following figure:

The other triangle has a $60^{\circ}$ interior angle, which does not meet the problem's requirements;
The other triangle has an interior angle of $150^{\circ}$,
In this case, the other two interior angles can be calculated as
$$
15^{\circ}, 135^{\circ} ;
$$

If the 30-degree interior angle is divided, as shown in the following figure:
Therefore, the sum of the interior angles: $a+2 b+d=180^{\circ}$, the relationship of the exterior angle: $a=2 b$, and $a+b=30^{\circ}$;
Thus, $a=20^{\circ}, b=10^{\circ}$, and the other interior angle is $140^{\circ}$;
In summary: There are two cases, the other two interior angles are $15^{\circ}, 135^{\circ}$ or $10^{\circ}, 140^{\circ}$.