PQRSTW is a regular hexagon and QS intersects RT at V. Calculate ∠TVS

  • A 120°
  • B 90°
  • C 30°
  • D 60°
jamb 2006mathematics

The correct answer is D. 60°

Each ∠of a regular polygon

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

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

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

= 120

ΔQSR is isosceles

∴ Q = S = 30

Also ΔTSR is isosceles

∴ T = R = 30

∠TSV + ∠VSR = 120

∠TSV + 30 = 120

∠TSV = 120 - 30

∠TSV = 90

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

30 + 90 + ∠TVS = 180

120 + ∠TVS = 180

∠TVS = 180 - 120

∠TVS = 60

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