1. **Problem Statement:** Find the measure of angle 7 given the expressions for two angles formed by intersecting lines: $3x + 90$ and $2x + 155$. 2. **Understanding the problem:** The two given expressions represent angles that are either vertical angles or corresponding angles formed by two parallel lines and a transversal. Such angles are equal. 3. **Set up the equation:** Since these angles are equal, $$3x + 90 = 2x + 155$$ 4. **Solve for $x$:** Subtract $2x$ from both sides: $$3x + 90 - \cancel{2x} = 2x + 155 - \cancel{2x} \implies x + 90 = 155$$ Subtract 90 from both sides: $$x + 90 - 90 = 155 - 90 \implies x = 65$$ 5. **Find the measure of angle 7:** Substitute $x=65$ into the expression for angle 7, which is $3x + 90$: $$3(65) + 90 = 195 + 90 = 285$$ 6. **Interpretation:** Angle 7 measures $285$ degrees. However, since angles around a point sum to $360$ degrees, and angle 7 is likely an exterior angle, we check if this is consistent. If angle 7 is an obtuse angle formed by the lines, $285$ degrees is possible. **Final answer:** $$\boxed{285}$$