You seem to generally have the right idea, and you seem to be able to solve the equations you write. However, your choice of equations for the problem sometimes needs a little work.
12.
Given
- ∠DBC = (12x -3)°
- ∠DBE = (5x +12)°
- ∠EBC = (3x +13)°
- ∠DBC = ∠DBE + ∠EBC
Find
Solution
∠DBC = ∠DBE + ∠EBC
(12x -3) = (5x +12) + (3x +13) . . . . . substitute given values
12x -3 = 8x +25 . . . . . . . . . collect terms
4x = 28 . . . . . . . . . . . . . . . add 3-8x
x = 7 . . . . . . . . . . . . . . . . . . divide by 4
3x +13 = 3·7 +13 = 34
∠EBC = 34°
__________
13.
Given
- ∠FBC = (10x -9)°
- ∠CBE = (4x +15)°
- ∠FBC = ∠CBE = (1/2)∠FBE
Find
Solution
∠FBC = ∠CBE
10x -9 = 4x +15 . . . . . substitute given values
6x = 24 . . . . . . . . . . . .add 9-4x
x = 4 . . . . . . . . . . . . . . divide by 4
∠FBC = (10·4 -9)° = 31°
∠FBE = 2·∠FBC = 2·31°
∠FBE = 62°
__________
14.
Given
- ∠1 = (7x -19)°
- ∠2 = (x +5)°
- ∠1 + ∠2 = 90°
Find
Solution
∠1 +∠2 = 90°
(7x -19) +(x +5) = 90 . . . . . . substitute the given values
8x -14 = 90 . . . . . . . . . . . . . collect terms
8x = 104 . . . . . . . . . . . . . . . add 14
x = 13 . . . . . . . . . . . . . . . . . . divide by 8
∠2 = (13 +5)°
∠2 = 18°
__________
15.
Given
- ∠1 = (6x +25)°
- ∠4 = (10x -11)°
- ∠1 = ∠4 . . . . . . they are vertical angles
Find
Solution
∠1 = ∠4
6x +25 = 10x -11 . . . . substitute the given values
36 = 4x . . . . . . . . . . . add 11-6x
9 = x . . . . . . . . . . . . . .divide by 4
∠1 = (6·9 +25)°
∠1 = 79° . . . . . . matches your answer
