PQRSTU is a regular hexagon . Determine each angle of triangle PQT
Consider the regular hexagon inscribed in a circle.
Consider ΔPOQ, we know that each triangle in a regular hexagon made from the centre is equilateral.
So, ∠POQ = ∠OQP = ∠QPO = 60°
∠PTQ = ∠POQ [Angle made by an arc on the circle is half the angle made by the same arc on the centre]
PO = OT = radius of circle
∴ ∠OPT = ∠OTP = 30° [Angles opposite to equal sides are equal]
Now, in ΔPQT,
∠TPQ = ∠TPO + ∠OPQ
= 30° + 60°
∠TQP = 60°
∠PTQ = 30°
Thus, angles of ΔPQT are 90°, 60° and 30°.