Answer:
m∠DEF = 135º
Step-by-step explanation:
1. I will find the answer to X by writing what ∠FEA, ∠AEB, ∠BEC by doing
(2x+5) + (4x) + (3x-5) = 180, all simplified it will give me x=20
2. I want to figure out what ∠AEB and ∠BEC are
since x=20 and ∠AEB is 4x, we substitute x as 20 as : 4(20) which is 80.
We then figure out ∠BEC since x=20 and ∠BEC is 3x-5 we substitute the 20 in place of x, which will be 3(20) - 5= 55.
3. I want to add ∠AEB + ∠BEC to get the vertical angle of ∠DEF
(the vertical angel of ∠DEF is ∠AEB + ∠BEC)
∠AEB + ∠BEC = ∠DEF
80 + 55 = ∠DEF
135 = ∠DEF
