1. The problem asks to find the measure of angle 1, denoted as $m \angle 1$, in a triangle where two angles are given as 87° and 145°. 2. Recall the Triangle Angle Sum Theorem: The sum of the interior angles of a triangle is always 180°. This can be written as: $$m \angle 1 + 87^\circ + 145^\circ = 180^\circ$$ 3. Add the known angles: $$87^\circ + 145^\circ = 232^\circ$$ 4. Substitute back into the equation: $$m \angle 1 + 232^\circ = 180^\circ$$ 5. To find $m \angle 1$, subtract 232° from both sides: $$m \angle 1 = 180^\circ - 232^\circ = -52^\circ$$ 6. Since an angle in a triangle cannot be negative, this indicates an error: the sum of the two given angles exceeds 180°, which is impossible for a triangle. 7. Therefore, the given angles 87° and 145° cannot both be interior angles of the same triangle, and $m \angle 1$ cannot be found under these conditions.