Question

24. PQRSTU is a regular hexagon. Determine each angle of APQT.​

Answer 1

Step-by-step explanation:

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:

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.