JAMB - Mathematics (1993 - No. 42)

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

18^o

54^o

90^o

108^o

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 = \(\frac{360}{4} = 90°\)

\(PTU + TPU + TUP = 180°\)

\(108° + (180° - 90°) + TUP = 180°\)

\(TUP = 180° - (108° + 18°) = 54°\)