Question

Given PQRS is a square, solve for x.

Answer 1

Answer:

x = 11

Step-by-step explanation:

The angles in a square are right , that is 90°

The diagonals bisect the angles , then

6x - 21 = 45 ( add 21 to both sides )

6x = 66 ( divide both sides by 6 )

x = 11

Answer 2

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