Answer:
The answer to your question is:
2.-
a) ∠ACB + ∠ ACE = 7x + 54
b) ∠ACB = 115° ∠ ACE = 65°
3.-
a) They measure the same
b) ∠MFG = ∠EFN = 80°
Step-by-step explanation:
1.- ∠ACB and ∠ ACE are linear pairs so ∠ACB + ∠ ACE = 180
∠ACB = 5x + 25
∠ ACE = 2x + 29
∠ACB + ∠ ACE = 180 = 5x + 25 + 2x + 29
180 = 7x + 54
7x + 54 = 180
7x = 180 -54
7x = 126
x = 126 / 7
x = 18
Then ∠ACB = 5(18) + 25 = 115° ∠ ACE = 2(18) + 29 = 65
2.- ∠MFG ∠EFN are vertical angles
∠MFG = 7x - 18 ∠EFN = 5x + 10
They measure the same, then
7x - 18 = 5x + 10
7x - 5x = 18 + 10
2x = 28
x = 28/2
x = 14
∠MFG = 7(14) - 18 = 98 - 18 = 80 ∠EFN = 5(14) + 10 = 70 + 10 = 80
