1. The problem asks for the measure of angle 1, denoted as $m\angle 1$. 2. We are given a triangle with angles 100°, 30°, and angle 1 at the top vertex. 3. Recall the Triangle Angle Sum Theorem: The sum of the interior angles of a triangle is always 180°. 4. Using the theorem, we write the equation: $$100^\circ + 30^\circ + m\angle 1 = 180^\circ$$ 5. Simplify the left side: $$130^\circ + m\angle 1 = 180^\circ$$ 6. Subtract 130° from both sides to isolate $m\angle 1$: $$m\angle 1 = 180^\circ - 130^\circ$$ 7. Calculate the difference: $$m\angle 1 = 50^\circ$$ Therefore, the measure of angle 1 is $50^\circ$.