PQRST is a regular pentagon and PQVU is a rectangle with U and V lying…

PQRST is a regular pentagon and PQVU is a rectangle with U and V lying on TS and SR respectively as shown in the diagram. Calculate TUP

  • A.
    18o
  • B.
    54o
  • C.
    90o
  • D.
    108o
Correct Answer: Option B
Explanation

The total angle in a regular pentagon = ((2(5) – 4) times 90)

= (6 times 90 = 540°)

Each interior angle = (frac{540}{5} = 108°)

While the interior of a quadrilateral = (frac{360}{4} = 90°)

(PTU + TPU + TUP = 180°)

(108° + (180° – 90°) + TUP = 180°)

(TUP = 180° – (108° + 18°) = 54°)

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