Question

PQRSTU is a regular hexagon.Find each angle of ∆PQT.(please explain it to me)

Answer 1

Properties of hexagon:                  

Angle tup = 120 degrees

tu = up

Therefore angle utp = angle upt = 30 degrees (two sides being

equal, corresponding angles equal)

So angle tpq = 90 degrees

Draw a mid-point ‘a’ on tp

Pt = 2* ta                                                         

tan (angle tqp) = tp / pq

    = 2* tu * cos 30                                                           

= square root 3x / x

    = 2 * x * square

root 3 / 2                                             = square

root 3

    = square root 3x                                 Therefore, angle tqp =

60 degrees

So the angles are : angle tpq = 90 degrees , angle tqp = 60

degrees and angle ptq = 30 degrees.

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