Question

PQRSTU is a regular hexagon.determine each angle of triangle PQT .

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.

Answer 2

Answer:

90 ,60,45 is the three angles