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 = \((2(5) - 4) \times 90\)
= \(6 \times 90 = 540°\)
Each interior angle = \(\frac{540}{5} = 108°\)
While the interior of a quadrilateral = \(\frac{360}{4} = 90°\)
\(PTU + TPU + TUP = 180°\)
\(108° + (180° - 90°) + TUP = 180°\)
\(TUP = 180° - (108° + 18°) = 54°\)