The sum of interior angles of a polygon = (n – 2) × 180°
The sum of interior angles of a hexagon = (6 – 2) × 180° = 4 × 180° = \(\frac{720°}{6}\)
Measure of each angle of hexagon = \(\frac{720°}{6}\) = 120°
∠PUT = 120° Proved above
In Δ PUT
∠PUT + ∠UTP + ∠TPU = 180° [Angle sum property of a triangle]
120° + 2∠UTP = 180° [Since ΔPUT is isosceles triangle]
2∠UTP = 180° - 120°
∠UTP = \(\frac{60°}{2}\) = 30°
∠UTP = ∠TPU = 30°
Similarly ∠RTS = 30°
Therefore ∠PTR = ∠UTS - ∠UTP - ∠RTS
∠PTR = 120° - 30° - 30° = 120° - 60° = 60°
∠TPQ = ∠UPQ - ∠UPT
∠TPQ = 120° - 30° = 90°
∠TQP = 180° - 150° = 30°[Using angle sum property of triangle in ΔPQT]
