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In the diagram above, PQT is an isosceles triangle.|PQ| = |QT|, ∠SRQ = 75°, ∠QPT...

Mathematics
WAEC 1992

In the diagram above, PQT is an isosceles triangle.|PQ| = |QT|, ∠SRQ = 75°, ∠QPT = 25° and PQR is straight line. Find ∠RST

  • A. 20o
  • B. 50o
  • C. 55o
  • D. 70o
  • E. 75o
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Correct Answer: Option C
Explanation

< PTQ = 25° (base angles of an isos. triangle)

\(\therefore\) < PQT = 180° - (25° + 25°) = 130° (sum of angles in triangle PQT)

\(\therefore\) < RST = 130° - 75° = 55° (exterior angle = sum of 2 opp. interior angles)


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