Question

what is qt? qt =

Explanation:

Step1: Identify right - angled triangles

We have two right - angled triangles $\triangle QTS$ and $\triangle QRS$. Since $\angle T=\angle R = 90^{\circ}$ and $\angle TQS=\angle RQS$ (common angle) and $QS$ is common to both triangles.

Step2: Apply AAS (Angle - Angle - Side) congruence

By AAS congruence criterion, $\triangle QTS\cong\triangle QRS$.

Step3: Use congruent - triangle properties

In congruent triangles, corresponding sides are equal. So $QT = QR$.

Step4: Find the value of $QT$

Given $QR = 85$, so $QT=85$.

Answer:

85