In the diagram, PQ is a straight line, (m + n) = 110(^o) and (n + r) = 130(^o) and (m + r) = 120(^o). Find the ratio of m : n : r
-
A.
2 : 3 : 4 -
B.
3 : 4 : 5 -
C.
4 : 5 : 6 -
D.
5 : 6 : 7
Correct Answer: Option D
Explanation
m + n = 110(^o), (n + r) = 130(^o)
(m + n) = 120(^o)
then, r = 130(^o) – n
and;
m + (130^o – n) = 120(^o)
m – n = -10(^o)
2m + (n + r) = 110 + 120 = 230
2m + 130 = 230
2m = 230 – 130
m = (frac{100}{2}) = 50(^o)
n = 110(^o) – 50(^o)
= 60(^o)
r = 130(^o) – 60(^o) = 70(^o)
Hence, the ratio m : n : r
= 50 : 60 : 70
= 5 : 6 : 7