Step-by-step explanation:
In the given figure, we can see that there is a square, and know that diagonals of squares bisect each other at 90° , so
Angle PTQ = 90°
( since they bisects each other at 90° )
now,
since the diagonals of the square are equal and they are bisected by each other so,
PT = TQ
then, Angle TPQ = Angle TQP
( since, PT = TQ , Opposite sides are equal )
In triangle PTQ ,
Angle TQP + Angle TPQ + Angle PTQ = 180°
( since, sum of all interior angles of a triangle is 180° )
=》Angle TQP + Angle TPQ + 90° = 180°
( PTQ = 90° )
=》2 × Angle TQP = 90°
( TPQ = TQP )
=》TQP = 45°
From here,
TQP = 45° = 6x - 21
=》6x - 21 = 45°
=》6x = 45 + 21
=》6x = 66
=》x = 66 / 6
=》x = 11
