Question

1. if rs bisects ∠urt, m∠trs=(12x - 5)°, and m∠urt=(20x + 2)°, find m∠urs

m∠urs =

Explanation:

Step1: Use angle - bisector property

Since $\overline{RS}$ bisects $\angle URT$, then $m\angle TRS=\frac{1}{2}m\angle URT$. So, $2(12x - 5)=20x+2$.

Step2: Expand the left - hand side

Expand $2(12x - 5)$ to get $24x-10$. The equation becomes $24x - 10=20x+2$.

Step3: Isolate the variable terms

Subtract $20x$ from both sides: $24x-20x - 10=20x-20x + 2$, which simplifies to $4x-10 = 2$.

Step4: Solve for $x$

Add 10 to both sides: $4x-10 + 10=2 + 10$, so $4x=12$. Then divide both sides by 4: $x = 3$.

Step5: Find $m\angle URS$

Since $m\angle TRS=12x - 5$ and $m\angle URS=m\angle TRS$ (because $\overline{RS}$ is the angle - bisector), substitute $x = 3$ into $m\angle TRS$. $m\angle URS=12\times3-5=36 - 5=31^{\circ}$.

Answer:

$31^{\circ}$