1. **Problem Statement:** We are given a five-pointed star with angles at vertices B and D as 46° and 33° respectively, and we need to find the measure of angle $x$ at vertex H. 2. **Understanding the Star and Angles:** A five-pointed star is formed by extending the sides of a regular pentagon or by connecting points in a specific order. The key property is that the sum of the angles around each intersection point and the relationships between the angles in the star can be used to find unknown angles. 3. **Key Formula and Rules:** The sum of the interior angles of a pentagon is $$(5-2) \times 180^\circ = 540^\circ$$. The star is formed by extending sides, so the exterior angles and the angles at intersections relate to these interior angles. 4. **Using the Given Angles:** The angles at B and D are given as 46° and 33°. The angle $x$ at H is formed by the intersection of lines related to these points. 5. **Angle Relationships in the Star:** The angle at H, $x$, is supplementary to the sum of angles at B and D because they form a straight line or linear pair with $x$ in the star's geometry. 6. **Calculate $x$:** $$x = 180^\circ - (46^\circ + 33^\circ)$$ $$x = 180^\circ - 79^\circ$$ $$x = 101^\circ$$ 7. **Final Answer:** The measure of angle $x$ is $$\boxed{101^\circ}$$. This uses the property that angles on a straight line sum to 180°, and the given angles at B and D help find the unknown angle at H.