1. **State the problem:** We are given several algebraic and geometric expressions involving $x$ and angles, and we need to solve for $x$ and find the measure of angle $\angle CXY$. 2. **Solve the algebraic equations step-by-step:** - From the first equation: $10x = 72$ $$x = \frac{72}{10} = 7.2$$ - Next, the expression $3x - 4$ is given but not equated yet. - Then, the equation $3x - 4 = 10x - 72$ is given: $$3x - 4 = 10x - 72$$ Move all terms to one side: $$3x - 4 - 10x + 72 = 0$$ $$-7x + 68 = 0$$ $$-7x = -68$$ $$x = \frac{68}{7} \approx 9.714$$ - Next, $-4x - 8 = 4y - 72$ is given but $y$ is unknown, so we skip this. - Then, $64 = 4x$: $$x = \frac{64}{4} = 16$$ - Another solution for $x$ is given as $x=16$. 3. **Solve the angle equations:** - Given angles $(8x - 3)^\circ$ and $(16x - 33)^\circ$ and the equation: $$8x - 3 = 16x - 33$$ Move terms: $$8x - 3 - 16x + 33 = 0$$ $$-8x + 30 = 0$$ $$-8x = -30$$ $$x = \frac{30}{8} = 3.75$$ 4. **Find $m\angle CXY$ given $48^\circ$ and $89^\circ$ and $XY \parallel DE$:** - Since $XY \parallel DE$, $\angle DEY$ is the exterior angle to the triangle formed by angles $48^\circ$ and $89^\circ$. - Use the angle sum property of a triangle: $$\angle DEY = 180 - (48 + 89) = 180 - 137 = 43^\circ$$ **Final answers:** - From the first equation, $x = 7.2$ - From the second equation, $x \approx 9.714$ - From the third, $x = 16$ - From the angle equation, $x = 3.75$ - Measure of $\angle CXY = 43^\circ$