Question

if (mangle pqs = mangle rqs = 70^{circ}, ps = w + 6,) and (rs = 11w - 94,) what is (ps?)

Explanation:

Step1: Apply angle - bisector theorem

Since $\angle PQS=\angle RQS$ and $\angle P = \angle R=90^{\circ}$, by the angle - bisector theorem, $PS = RS$.

Step2: Set up the equation

Set $w + 6=11w-94$.

Step3: Solve for $w$

Subtract $w$ from both sides: $6 = 10w-94$. Then add 94 to both sides: $100 = 10w$. Divide both sides by 10, we get $w = 10$.

Step4: Find $PS$

Substitute $w = 10$ into the expression for $PS$. $PS=w + 6=10 + 6=16$.

Answer:

$16$