Question

rt bisects ∠qrs. if m∠trs = (-5x + 127)° and m∠qrt = (-x + 87)°, find the value of x.

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{RT}$ bisects $\angle QRS$, then $m\angle TRS=m\angle QRT$. So, $- 5x + 127=-x + 87$.

Step2: Add $5x$ to both sides

$-5x + 127+5x=-x + 87+5x$. This simplifies to $127 = 4x+87$.

Step3: Subtract 87 from both sides

$127 - 87=4x+87 - 87$. We get $40 = 4x$.

Step4: Divide both sides by 4

$\frac{40}{4}=\frac{4x}{4}$. Thus, $x = 10$.

Answer:

$x = 10$