In the given diagram, \(\bar{QT}\) and \(\bar{PR}\) are straight lines, < ROS = (3n - 20), < SOT = n, < POL = m and < QOL is a right angle. Find the value of n.
Attached Figure / Diagram
A
35o
B
40o
C
55o
D
60o
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
In the diagram, QOR + 2m(vertically opposite angles)
So, m + 90^\circ + 2m = 180^\circ
(angles on str. line)
3m = 180^\circ - 90^\circ
3m = 90^\circ
m = \(\frac{90^o}{3}\)
= 30^\circ
substituting 30^\circ for m in
2m + 4n = 200^\circ gives
2 x 30^\circ + 4n = 200^\circ
60^\circ + 4n = 200^\circ
4n = 200^\circ - 60^\circ
= 140^\circ
n = \(\frac{140^\circ}{4}\)
= 35^\circ
Source: Myschool Past Questions Archive (Record #45861)