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In the diagram, \(\bar{PF}\), \(\bar{QT}\), \(\bar{RG}\) intersect at S and PG||...


Question

In the diagram, \(\bar{PF}\), \(\bar{QT}\), \(\bar{RG}\) intersect at S and PG||RG. If < SPQ = 113o and < RST = 220o, find < PSQ.

Options

A) 22o

B) 45o

C) 67o

D) 89o

The correct answer is B.

Explanation:

In In the diagram given, \(\alpha\) = 22\(^{\circ}\) (vertically opp. angles), \(\alpha\) = \(\beta\) (alternate angles)
< PSQ + 133\(^{\circ}\) + \(\beta\) = 180\(^{\circ}\) (sum of angles of a \(\Delta\))
< PSQ + 133\(^{\circ}\) + 22\(^{\circ}\) = 180\(^{\circ}\)
< PSQ = 180\(^{\circ}\) - (133 + 22)\(^{\circ}\)
45\(^{\circ}\)

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Dicussion (1)

  • In In the diagram given, \(\alpha\) = 22\(^{\circ}\) (vertically opp. angles), \(\alpha\) = \(\beta\) (alternate angles)
    < PSQ + 133\(^{\circ}\) + \(\beta\) = 180\(^{\circ}\) (sum of angles of a \(\Delta\))
    < PSQ + 133\(^{\circ}\) + 22\(^{\circ}\) = 180\(^{\circ}\)
    < PSQ = 180\(^{\circ}\) - (133 + 22)\(^{\circ}\)
    45\(^{\circ}\)

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