Question: 5. P K J L 7. A B C 8. F G 9. Find the following angle measures and classify them based on their measures. m\angle BAC: Classification: m\angle DAE: Classification: m\angle EAC: Classification: 10. Solve for x. 2x - 10 2x - 16 10 11. BD has a point C between points B and D. BC = 7x - 4, CD = 3x + 1, and BD = 9x. Solve for x and find BC, CD, and BD.

1. **State the problem:** We are given that point C lies between points B and D on segment BD. The lengths are given as: $$BC = 7x - 4$$ $$CD = 3x + 1$$ $$BD = 9x$$ We need to solve for $x$ and then find the lengths of $BC$, $CD$, and $BD$. 2. **Use the Segment Addition Postulate:** The postulate states that if point C is between B and D, then: $$BC + CD = BD$$ 3. **Set up the equation:** $$7x - 4 + 3x + 1 = 9x$$ 4. **Simplify the left side:** $$7x + 3x - 4 + 1 = 9x$$ $$10x - 3 = 9x$$ 5. **Isolate $x$:** $$10x - 3 = 9x$$ Subtract $9x$ from both sides: $$10x - 9x - 3 = 0$$ $$x - 3 = 0$$ Add 3 to both sides: $$x = 3$$ 6. **Find the lengths:** Calculate $BC$: $$BC = 7(3) - 4 = 21 - 4 = 17$$ Calculate $CD$: $$CD = 3(3) + 1 = 9 + 1 = 10$$ Calculate $BD$: $$BD = 9(3) = 27$$ 7. **Check the result:** Verify that $BC + CD = BD$: $$17 + 10 = 27$$ This is true, so the solution is correct. **Final answer:** $$x = 3, BC = 17, CD = 10, BD = 27$$