Question

Question #01306

Answer 1

`x=30^circ`

Explanation:

I'm basing this solely on angle rules, not much else I can do for this. Someone may be able to provide a visual way of showing this.

Let's call the intersection `O`.

We know that the angles in a triangle add up to `180^circ`.

`/_AEB=180-(25+55+45)=180-125=55^circ`
`/_ADB=180-(35+55+45)=180-135=45^circ`
`/_AOB=180-(55+45)=180-100=80^circ`

Using the opposite angle rule, we know `/_EOD=/_AOB`

`/_OED=180-(x+80)=180-80-x=100-x`

Since angles on a straight line add up to `180^circ`:
`/_DEF=180-(100-x+55)=x+25`

`/_AFB=180-(25+35+45+55)=50^circ`

`/_FDE=180-(50+25+x)=105-x`

`/_EDO=180-(45+x+105-x)=30=x`