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In the diagram, PQR is a straight line, QRST is a parallelogram, < TPQ =...

Mathematics
WAEC 2006

In the diagram, PQR is a straight line, QRST is a parallelogram, < TPQ = 72o and < RST = 126o. What type of triangle is \(\bigtriangleup\) PQT?

  • A. An equilateral triangle
  • B. A right-angled triangle
  • C. An isosceles triangle
  • D. A scalene triangle
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Correct Answer: Option C
Explanation

< TSR = <RQT (opposite angles of a parallelogram are equal)

< PQT = 180º - 126º = 54º

<PTQ = 180º - 72º - 54º = 54º

Therefore, Angle PTQ is isosceles.

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