Question #01306

1 Answer
Dec 20, 2017

x=30

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.

AEB=180(25+55+45)=180125=55
ADB=180(35+55+45)=180135=45
AOB=180(55+45)=180100=80

Using the opposite angle rule, we know EOD=AOB

OED=180(x+80)=18080x=100x

Since angles on a straight line add up to 180:
DEF=180(100x+55)=x+25

AFB=180(25+35+45+55)=50

FDE=180(50+25+x)=105x

EDO=180(45+x+105x)=30=x