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In the figures, PQ is a tangent to the circle at R and UT is...

Mathematics
WAEC 2014

In the figures, PQ is a tangent to the circle at R and UT is parallel to PQ. if < TRQ = xo, find < URT in terms of x

  • A. 2xo
  • B. (90 - x)o
  • C. (90 + x)o
  • D. (180 - 2x)o
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Correct Answer: Option D
Explanation

< URT = < TRQ (angle alternate a tangent and a chord equal to angle in the alternate segment)

< RUT = xo

In \(\bigtriangleup\) URT

< RUT + < RUT + < UTR = 180o (sum of int. < s of \(\bigtriangleup\))

< URT + x + x = 180o

< URT = 180o - 2x

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