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POQ will be a straight line if
|_POR + |_QOR = 180°
=> (4x + 38°28') + (2x - 20°46') = 180°
=> 4x + 2x + 38°28' - 20°46' = 180°
=> 6x + (38 + 28'/60 )° - (20 + 46'/60)°= 180°
=> 6x + 577/15° - 623/30° = 180°
=> 6x + 177/10° = 180°
=> 6x = 180 - 17.7
=> 6x = 162.3
=> x = 162.3/6 = 27.05
Hence, x = 27.05 will make POQ a straight line.
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