Question #01306

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Answer 1 · 2017-12-20T18:52:18

#x=30^circ#

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#