Mathematics

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

PQRSTW is a regular hexagon and QS intersects RT at V. Calculate ∠TVS
  • A.
    120o
  • B.
    90o
  • C.
    30o
  • D.
    60o
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