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

Explanation

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