Question

HELP!!!!
I lowkey need help!!!

Answer 1

`\boxed {x = 4}`

`\boxed {\angle 1 = 41\textdegree}`

`\boxed {\angle 2 = 139\textdegree}`

`\boxed {\angle 3 = 41\textdegree}`

`\boxed {\angle 4 = 139\textdegree}`

Explanation:

Both
`\angle 1` and
`\angle 3` are Vertical Angles. So, to the find actual measurement both of angles, you need to write an expression by using the following measurements labeled on both
`\angle 1` and
`\angle 3`, and solve for
`x`:

`\angle 1 = 8x + 9`

`\angle 3 = 14x - 15`

`8x + 9 = 14x - 15`

-Solve:

`8x + 9 = 14x - 15`

`8x + 9 - 14x = 14x - 14x - 15`

`-6x + 9 = -15`

`-6x + 9 = -15 - 9`

`-6x = -24`

`(-6x)/(-6) = (-24)/(-6)`

`\boxed {x = 4}`

After you have the value of
`x`, use it to find the actual measurement of
`\angle 1`and
`\angle 3`:

-The value of
`x`:

`x = 4`

-Finding the measurement of
`\angle 1`:

`8x + 9`

`8(4) + 9`

`32 + 9`

`41`

`\boxed {\angle 1 = 41\textdegree}`

-Finding the measurement of
`\angle 3`:

`14x - 15`

`14(4) - 15`

`56 - 15`

`41`

`\boxed {\angle 3 = 41\textdegree}`

After you have the actual measurements of
`\angle 1` and
`\angle 3`, find the actual measurements of
`\angle 2` and
`\angle 4`.
`\angle 1` and
`\angle 2` are both supplementary (two angle that add up to
`180\textdegree`), you need to find the measurement of
`\angle 2` by subtracting the measurement of
`\angle 1` from
`180\textdegree`. Same thing for
`\angle 3` and
`\angle 4`:

-Finding the measurement of
`\angle 2`:

`180\textdegree - \angle 1`

`180\textdegree - 41\textdegree`

`139\textdegree`

`\boxed {\angle 2 = 139\textdegree}`

-Finding the measurement of
`\angle 4`:

`180\textdegree - \angle 3`

`180\textdegree - 41\textdegree`

`139\textdegree`

`\boxed {\angle 4 = 139\textdegree}`

And were done.