PQRSTW is a regular hexagon and QS intersects R... - JAMB Mathematics 2006 Question

Each ∠of a regular polygon

(=\frac{(n-2)180}{n}\

=\frac{(6-2)180}{6}\

=\frac{(4)180}{6})

= 120^o

ΔQSR is isosceles

∴ Q = S = 30^o

Also ΔTSR is isosceles

∴ T = R = 30^o

∠TSV + ∠VSR = 120

∠TSV + 30 = 120

∠TSV = 120 - 30

∠TSV = 90^o

∴∴VTS + ∴VST + ∴TVS = 180 (sum of ∠s of a Δ)

30 + 90 + ∠TVS = 180

120 + ∠TVS = 180

∠TVS = 180 - 120

∠TVS = 60^o