Question

use any theorems, postulates, or properties to solve for x. 9) 10) 12x - 4 80° 12x - 3 10x + 15

Explanation:

Step1: Identify angle - relationship in 9)

The two angles are vertical angles. Vertical angles are equal. So we set up the equation $12x - 4=80$.

Step2: Solve the equation for 9)

Add 4 to both sides: $12x=80 + 4=84$. Then divide both sides by 12: $x=\frac{84}{12}=7$.

Step3: Identify angle - relationship in 10)

The two angles are corresponding angles (assuming the lines are parallel). Corresponding angles are equal. So we set up the equation $12x-3 = 10x + 15$.

Step4: Solve the equation for 10)

Subtract $10x$ from both sides: $12x-10x-3=10x - 10x+15$, which simplifies to $2x-3 = 15$. Add 3 to both sides: $2x=15 + 3=18$. Divide both sides by 2: $x=\frac{18}{2}=9$.

Answer:

For 9), $x = 7$; for 10), $x = 9$