2006
Mathematics
67ca00ce0c643c71d77dee1f
PQRSTW is a regular hexagon and QS intersects RT at V. Calculate ∠TVS
A.
120°
B.
90°
C.
30°
D.
60°
Correct Answer: 60°
Explanation
Each ∠of a regular polygon=((n-2)180)/n=((6-2)180)/6=((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°
Each ∠of a regular polygon=((n-2)180)/n=((6-2)180)/6=((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°THIS WEEK's
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