1. The problem asks to find the measure of angle 1 (m\angle 1) in a triangle where the other two angles are 53° and 150°. 2. Recall the Triangle Angle Sum Theorem: The sum of the interior angles of a triangle is always 180°. 3. Using the theorem, we write the equation: $$m\angle 1 + 53° + 150° = 180°$$ 4. Combine the known angles: $$53° + 150° = 203°$$ 5. Substitute back: $$m\angle 1 + 203° = 180°$$ 6. Solve for $m\angle 1$: $$m\angle 1 = 180° - 203° = -23°$$ 7. Since an angle in a triangle cannot be negative, this indicates the given angles cannot form a triangle. Possibly, the 150° angle is an exterior angle or there is a mistake in the problem setup. Final answer: The given angles do not form a valid triangle, so $m\angle 1$ cannot be determined as a positive angle in this context.