In the diagram lt PSR 220o lt SPQ 58o and lt PQ... - WAEC Mathematics 2010 Question
In the diagram, < PSR = 220o, < SPQ = 58o and < PQR = 41o. Calculate the obtuse angle QRS.
A
90o
B
100o
C
121o
D
60o
correct option: c
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
(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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