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In the diagram, < PSR = 220o, < SPQ = 58o and < PQR =...

Mathematics
WAEC 2010

In the diagram, < PSR = 220o, < SPQ = 58o and < PQR = 41o. Calculate the obtuse angle QRS.
  • A. 90o
  • B. 100o
  • C. 121o
  • D. 60o
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Correct Answer: Option C
Explanation
Joining SQ. In \(\bigtriangleup\) SPQ,

(22o + a) + 55o + (41o + b) = 180o

121o + a + b = 180o

a + b = 180 - 121

a + b = 59o.....(1)

In \(\bigtriangleup\) SRPQ; R + a + b = 180o

R + 59o = 180o

(in (1), a + b = 59o)

R = 180 - 59

R = 121o

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