PQRSTW is a regular hexagon and QS intersects RT at V. Calculate ∠ TVS
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Correct Answer: Option D
Explanation:
Each ∠ of a regular polygon
\(=\frac{(n-2)180}{n}\\
=\frac{(6-2)180}{6}\\
=\frac{(4)180}{6}\)
= 120o
ΔQSR is isosceles
− Q = S = 30o
Also ΔTSR is isosceles
− T = R = 30o
∠ TSV + ∠ VSR = 120
∠ TSV + 30 = 120
∠ TSV = 120 - 30
∠ TSV = 90o
−−VTS + −VST + −TVS = 180 (sum of ∠ s of a Δ)
30 + 90 + ∠ TVS = 180
120 + ∠ TVS = 180
∠ TVS = 180 - 120
∠ TVS = 60o
Each ∠ of a regular polygon
\(=\frac{(n-2)180}{n}\\
=\frac{(6-2)180}{6}\\
=\frac{(4)180}{6}\)
= 120o
ΔQSR is isosceles
− Q = S = 30o
Also ΔTSR is isosceles
− T = R = 30o
∠ TSV + ∠ VSR = 120
∠ TSV + 30 = 120
∠ TSV = 120 - 30
∠ TSV = 90o
−−VTS + −VST + −TVS = 180 (sum of ∠ s of a Δ)
30 + 90 + ∠ TVS = 180
120 + ∠ TVS = 180
∠ TVS = 180 - 120
∠ TVS = 60o