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
Attached Figure / Diagram
A
2 : 3 : 4
B
3 : 4 : 5
C
4 : 5 : 6
D
5 : 6 : 7
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #49580)