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PQRST is a regular pentagon and PQVU is a rectangle with ...

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

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 is B

The total angle in a regular pentagon = (2(5)4)×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°