Question

Solve for x and y. Then find the angle measures.X =Y=

Answer 1

x=40°, y=35°

Step-by-step explanation:

In the diagram

• Angles 3x+5 and 4y-15 are vertically opposite angles.

,

• Angles y+20 and x+15 are also vertically opposite.

Since vertical angles are equal, we have the following.

`\begin{gathered} 3x+5=4y-15 \\ y+20=x+15 \end{gathered}`

We solve the two equations above for x and y.

From the second equation:

`\begin{gathered} y=x+15-20 \\ y=x-5 \end{gathered}`

Substitute y=x-5 into the first equation.

`\begin{gathered} 3x+5=4(x-5)-15 \\ 3x+5=4x-20-15 \\ 3x+5=4x-35 \\ 4x-3x=5+35 \\ x=40^0 \end{gathered}`

We then solve for y.

`\begin{gathered} y=x-5 \\ =40-5 \\ =35^0 \end{gathered}`