Question

How do I solve this?

Answer 1

`x=9\\y=41\\m\angle EBF = 56^\circ`

Explanation:

Finding x is not too bad since it's clear that
`\angle ABD` and
`\angle DBC` are complementary angles, which add up to 90°:

`m\angle ABD+m\angle DBC=90^\circ\\(3x+7)^\circ+(5x+11)^\circ=90^\circ\\3x+7+5x+11=90\\8x+18=90\\8x=72\\x=9`

Given we now know the value of x, we can use that information to solve for y by recognizing that
`\angle DBC` and
`\angle FBC` are supplementary angles, which add up to 180°:

`m\angle DBC+m\angle FBC=180^\circ\\(5x+11)^\circ+(3y+1)^\circ=180^\circ\\5x+11+3y+1=180\\5(9)+11+3y+1=180\\45+11+3y+1=180\\3y+57=180\\3y=123\\y=41`

Lastly, we can figure out
`m\angle EBF` since both that and
`\angle DBC` are vertical angles, meaning they have the same angle measure. Since
`m\angle DBC=(5(9)+11)^\circ=(45+11)^\circ=56^\circ`, then
`m\angle EBF=56^\circ` as well.

I hope this helped! Feel free to comment below if I need to expand on anything that you may have not understood.