(a)
In the diagram above, $\theta =y$ (vertically opposite angles)
$\alpha =180°-110°=70°$ (angles on a straight line)
Thus, $\beta =\theta +\alpha$ (sum of interior opp. angles)
$\beta =y+70°.....(1)$
$x+r+\beta =180°.....(2)$
But 2x = r = y
Hence, $x+2x+(2x+70)=5x+70=180$
$5x=180-70=110$
$x=22°$
(b) Let Nx represent the donation collected by the girls. Then, the donation collected by the boys = N(x + 600).
Also, let y represent the average collection, $x_g$, of the girls. Then the average collection, $x_b$, of the boys = N(y + 100).
Thus, $x_g=\frac{x}{12}=y$
$x=12y...(1)$
$x_b=\frac{x+600}{10}=y+100$
$x+600=10(y+100)....(2)$
Substitute 12y for x in (2) :
$12y+600=10y+1000$
$12y-10y=1000-600$
$2y=400⟹y=200$
From (1), $x=12y$
$\therefore x=12\times 200=N2,400$.
Thus, the girls collected N2,400
The boys collected N2,400 + N600 = N3000
Total = N(2,400 + 3,000) = N5,400