In the given diagram, \(\bar{QT}\) and \(\bar{PR}\) are straight lines, &lt; ROS = (3n -...

In the given diagram, \(\bar{QT}\) and \(\bar{PR}\) are straight lines, < ROS = (3n -...

WAEC 2015

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.

A. 35^o
B. 40^o
C. 55^o
D. 60^o

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Correct Answer: Option A

Explanation

In the diagram, QOR + 2m(vertically opposite angles)

So, m + 90° + 2m = 180°

(angles on str. line)

3m = 180° - 90°

3m = 90°

m = \(\frac{90^o}{3}\)

= 30°

substituting 30° for m in

2m + 4n = 200° gives

2 x 30° + 4n = 200°

60° + 4n = 200°

4n = 200° - 60°

= 140°

n = \(\frac{140°}{4}\)

= 35°