Explanation

(a)

(i)

< NPQ = 180\(^o\) - 50\(^o\) = 130\(^o\)

< MNP = 130\(^o\) - 90\(^o\) = 40\(^o\)

< NMP = 40\(^o\) (Isolceles triangle) 

< MNP = 180\(^o\) - (40\(^o\) + 40\(^o\))

= 180\(^o\) - 80\(^o\) = 100\(^o\)

(ii) < OPQ = 90\(^o\)(50\(^o\) - 40\(^o\)) = 80\(^o\)

< OPQ = 80\(^o\) (Isoseles triangle) 

< POQ = 180\(^o\) (80\(^o\) + 80\(^o\))

180\(^o\) - 160\(^o\) = 20\(^o\) 

(b) 8y + 4x = 24

\(\frac{8y}{8} = \frac{-4y}{8} + \frac{24}{8}\) 

y = \(\frac{-1}{2}x + 6\)

m = \(\frac{-1}{2}\)

The equation will give 

\(\frac{y - 12}{x + 8} = \frac{-1}{2}\)

2y - 24 = x - 8 

2y = - x - 8 + 24

2y = -x + 16

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