Question

Find the value of the variables and the measure of each angle in the diagram

Answer 1

9.

(13x + 9)⁰ and (15x - 1)⁰ are vertical angles, therefore:

`13x+9=15x-1`

Solve for x:

`\begin{gathered} 15x-13x=9+1 \\ 2x=10 \\ x=(10)/(2) \\ x=5 \end{gathered}`

(4y + 2)⁰ and 2(3y - 25)⁰ are also vertical angles, so:

`\begin{gathered} 4y+2=2(3y-25) \\ 4y+2=6y-50 \end{gathered}`

Solve for y:

`\begin{gathered} 6y-4y=50+2 \\ 2y=52 \\ y=(52)/(2) \\ y=26 \end{gathered}`

Therefore:

`\begin{gathered} 13x+9=13(5)+9=74 \\ 15x-1=15(5)-1=74 \\ 4y+2=4(26)+2=106 \\ 2(3y-25)=2(3(26)-25)=2(53)=106 \end{gathered}`