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]

 

Consider ΔPOT,

PO = OT = radius of circle

∴ ∠OPT = ∠OTP = 30°  [Angles opposite to equal sides are equal]

Now, in ΔPQT,

∠TPQ = ∠TPO + ∠OPQ

= 30° + 60° 

= 90°

∠TQP = 60°

∠PTQ = 30°

Thus, angles of ΔPQT are 90°, 60° and 30°.

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