Answer:
Step-by-step explanation:
A) ∠1 = ∠2 {Alternate angles are equal}
6x + y - 4 = x - 9y + 1
6x + y = x - 9y + 1 + 4
6x + y = x - 9y + 5
6x - x + y + 9y = 5
5x + 10y = 5
Divide the entire equation by 5
x + 2y = 1 -------------(I)
∠2 + ∠3 = 180 {Linear pair}
x - 9y + 1 + 11x + 2 = 180
x + 11x - 9y = 180 - 2 - 1
12x - 9y = 177
Divide the whole equation by 3
4x - 3y = 59 -------------(II)
B) Multiply equation (I) by 3 and multiply equation (II) by 2. Thus y will be eliminated and we can find the value of x.
(I)* 3 3x + 6y = 3
(II)*2 8x - 6y = 118 {Now add}
11x = 121
x = 121/11
x = 11
Plugin x = 11 in equation (I)
11 + 2y = 1
2y = 1 -11
2y = -10
y = -10/2
y = -5
C) ∠1 = 6x + y - 4
= 6*11 - 5 - 4
= 66 - 5 - 4
= 57
∠2 = x - 9y + 1
= 11 -9*(-5) + 1
= 11 + 45 + 1
= 57
∠3 = 11x + 2
= 11*11 + 2
= 121 + 2
= 123
