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

Question

(1 point)

The measure of MRS is 55°.

The measure of MRS is 27.5".

The measure of MRS is 220°.

The measure of MRS is 110".

Check answer Remaining Attempts: 3

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Answer 1

To find the measure of angle MRS given that the measure of angle QRM is 55°, we can use the property of angle bisectors. An angle bisector divides the angle into two equal parts.

Since Remy constructed the angle bisector of angle QRS, we know:

• Measure of angle QRM = 55°
• Therefore, measure of angle MRS = measure of angle QRM = 55°

However, the angle QRS, which is being bisected, would have a total of:

• Measure of angle QRS = Measure of angle QRM + Measure of angle MRS
• Therefore, the measure of angle QRS = 55° + 55° = 110°

Thus, if the angle bisector is constructed, the angles QRM and MRS indeed are equal to one another.

So, the answer to the question is:

The measure of MRS is 55°.