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Home » Past Questions » Mathematics » In the given diagram, \(\bar{QT}\) and \(\bar{PR}\) are straight lines. Find n.

In the given diagram, \(\bar{QT}\) and \(\bar{PR}\) are straight lines. Find n.

Question

In the given diagram, \(\bar{QT}\) and \(\bar{PR}\) are straight lines. Find n.

Options

A)

35^o

B)

40^o

C)

55^o

D)

60^o

The correct answer is A.

Explanation:

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

SO, m + 90^o + 2m = 180^o

(angles on str. line)

3m = 180^o - 90^o

3m = 90^o

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

= 30^o

substituting 30^o for m in

2m + 4n = 200^o gives

2 x 30^o + 4n = 200^o

60^o + 4n = 200^o

4n = 200^o - 60^o

= 140^o

n = \(\frac{140^0}{4}\)

= 35^o

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Nigerian Scholars Follow5 years ago
In the diagram, QOR + 2m(vertically opposite angles)
SO, m + 90^o + 2m = 180^o
(angles on str. line)
3m = 180^o - 90^o
3m = 90^o
m = \(\frac{90^o}{3}\)
= 30^o
substituting 30^o for m in
2m + 4n = 200^o gives
2 x 30^o + 4n = 200^o
60^o + 4n = 200^o
4n = 200^o - 60^o
= 140^o
n = \(\frac{140^0}{4}\)
= 35^o
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