Question

in the diagram shown, it is given that $overline{tu}perpoverline{tw}$, $mangle utv = 61^{circ}$, and $mangle wtx=27^{circ}$. does $overline{tw}$ bisect $angle vtx$? explain how you arrived at your conclusion.

Explanation:

Step1: Find m∠WTU

Since $\overline{TU}\perp\overline{TW}$, $m\angle WTU = 90^{\circ}$.

Step2: Find m∠VTW

We know $m\angle UTV=61^{\circ}$, and $m\angle WTU = 90^{\circ}$. So $m\angle VTW=m\angle WTU - m\angle UTV=90^{\circ}- 61^{\circ}=29^{\circ}$.

Step3: Compare angles

We are given $m\angle WTX = 27^{\circ}$. Since $m\angle VTW=29^{\circ}$ and $m\angle WTX = 27^{\circ}$, $m\angle VTW
eq m\angle WTX$.

Answer:

No, $\overline{TW}$ does not bisect $\angle VTX$ because $m\angle VTW = 29^{\circ}$ and $m\angle WTX=27^{\circ}$, and for a ray to bisect an angle, it must divide the angle into two equal - measure angles.