Use the image to answer the question.

Question

Three rightward rays diverge from a vertex. Three arcs are drawn intersecting the rays.

Remy constructed the angle bisector of ∠QRS
as shown in the image. He measures the ∠QRM
as 55°
. What is the measure of ∠MRS
?

(1 point)
Responses

The measure of ∠MRS
is 55°
.
The measure of angle upper M upper R upper S is 55 degrees .

The measure of ∠MRS
is 27.5°
.
The measure of angle upper M upper R upper S is 27.5 degrees .

The measure of ∠MRS
is 110°
.
The measure of angle upper M upper R upper S is 110 degrees .

The measure of ∠MRS
is 220°
.

Answer 1

To determine the measure of ∠MRS, we can use the properties of angle bisectors.

Since Remy constructed the angle bisector of ∠QRS and measures ∠QRM as 55°, this means that the angle is split equally by the bisector. Therefore, ∠QRS is composed of two equal parts:

\[ ∠QRS = ∠QRM + ∠MRS = 55° + ∠MRS \]

Since the angle bisector divides the angle into two equal parts, we have:

\[ ∠QRM = ∠MRS = 55° \]

Thus, we can see that:

\[ ∠QRS = ∠QRM + ∠MRS = 55° + 55° = 110° \]

So ∠MRS, being equal to ∠QRM due to the angle bisector, is also:

\[ ∠MRS = 55° \]

Therefore, the measure of ∠MRS is 55°.

The correct response is: The measure of ∠MRS is 55°.