Question

angle bisector

the angle bisector is the ray that bisects an angle by dividing it into two congruent angles.

\\\angle trm \cong \angle mrq\\

if \\(m\angle qrt = 115^{\circ}\\), what is the measure of \\(\angle qrm\\) and \\(\angle trm\\)?

Explanation:

Identify the given information

We are given that the total angle measure is:

$$m\angle QRT = 115^\circ$$

The ray \(\overrightarrow{RM}\) is an angle bisector, which divides \(\angle QRT\) into two congruent angles:

$$\angle TRM \cong \angle MRQ$$

Apply the angle bisector definition

An angle bisector divides the total angle measure into two equal parts:

$$m\angle QRM = m\angle TRM = \frac{m\angle QRT}{2}$$

Calculate the measures of the bisected angles

Divide the total angle measure by \(2\):

$$\frac{115^\circ}{2} = 57.5^\circ$$

Therefore:

$$m\angle QRM = 57.5^\circ$$

$$m\angle TRM = 57.5^\circ$$

Answer:

If \(m\angle QRT = 115^\circ\), what is the measure of \(\angle QRM\) and \(\angle TRM\)?
The measure of \(\angle QRM\) is <blank>\(57.5^\circ\)</blank> and the measure of \(\angle TRM\) is <blank>\(57.5^\circ\)</blank>.