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

Question

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 110°
.
The measure of angle upper M upper R upper S is 110 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 220°
.

Answer 1

To find the measure of ∠MRS, we first need to understand the relationship between the angles involved.

Given that Remy constructed the angle bisector of ∠QRS and that ∠QRM is 55°, this means that the angle bisector divides ∠QRS into two equal parts. Therefore, we can denote:

• ∠QRM = 55° (as given)
• ∠MRS will be equal to ∠QRM since the angle bisector divides ∠QRS into two equal angles.

Since the angle bisector splits it into two equal angles, it follows that:

\[ ∠QRS = ∠QRM + ∠MRS \]

Since ∠QRM is 55°, the other part of the angle bisector (∠MRS) will also be 55°. Therefore:

\[ ∠MRS = 55° \]

Thus, the correct response is:

The measure of ∠MRS is 55°.