Question

1. solve for x. (6x - 21)° p q t s r

Explanation:

Step1: Identify square angle property

All interior angles of a square are $90^\circ$, so $\angle PQR = 90^\circ$.

Step2: Use diagonal angle bisector rule

The diagonal of a square bisects its interior angle, so $\angle PQT = \frac{1}{2}\angle PQR$.
Substitute values: $6x - 21 = \frac{1}{2} \times 90$

Step3: Simplify right-hand side

Calculate $\frac{1}{2} \times 90 = 45$, so $6x - 21 = 45$

Step4: Isolate the variable term

Add 21 to both sides: $6x = 45 + 21$
$6x = 66$

Step5: Solve for x

Divide both sides by 6: $x = \frac{66}{6}$

Answer:

$x = 11$