1. The measures of the angles of a triangle, expressed in degrees, represent three prime numbers. Find all possible values for the angles of this triangle.
1. If the measures of the angles of a triangle are three prime numbers, and their sum is $180^{\circ}$, not all three numbers can be odd, so one angle must measure $2^{\circ}$. Now we try prime numbers, in order, for the middle-sized angle, and check when the value of the remaining angle will also be a prime number. We find the following solutions: $\left\{2^{\circ}, 5^{\circ}, 173^{\circ}\right\},\left\{2^{\circ}, 11^{\circ}, 167^{\circ}\right\},\left\{2^{\circ}, 29^{\circ}, 149^{\circ}\right\},\left\{2^{\circ}, 41^{\circ}, 137^{\circ}\right\}$, $\left\{2^{\circ}, 47^{\circ}, 131^{\circ}\right\},\left\{2^{\circ}, 71^{\circ}, 107^{\circ}\right\}$ and $\left\{2^{\circ}, 89^{\circ}, 89^{\circ}\right\}$.