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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) 35o

B) 40o

C) 55o

D) 60o

The correct answer is A.

Explanation:

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

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

(angles on str. line)

3m = 180o - 90o

3m = 90o

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

= 30o

substituting 30o for m in

2m + 4n = 200o gives

2 x 30o + 4n = 200o

60o + 4n = 200o

4n = 200o - 60o

= 140o

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

= 35o


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Dicussion (1)

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

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

    (angles on str. line)

    3m = 180o - 90o

    3m = 90o

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

    = 30o

    substituting 30o for m in

    2m + 4n = 200o gives

    2 x 30o + 4n = 200o

    60o + 4n = 200o

    4n = 200o - 60o

    = 140o

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

    = 35o

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