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
Attached Figure / Diagram
A
18o
B
54o
C
90o
D
108o
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
The total angle in a regular pentagon = \((2(5) - 4) \times 90\)
= \(6 \times 90 = 540^\circ\)
Each interior angle = \(\frac{540}{5} = 108^\circ\)
While the interior of a quadrilateral = \(\frac{360}{4} = 90^\circ\)
\(PTU + TPU + TUP = 180^\circ\)
\(108^\circ + (180^\circ - 90^\circ) + TUP = 180^\circ\)
\(TUP = 180^\circ - (108^\circ + 18^\circ) = 54^\circ\)
Source: Myschool Past Questions Archive (Record #32993)