Answer:
100degrees
Step-by-step explanation:
Find the diagram attached
From the diagram
<PQT =<TRS = 40
Since the triangle STR is isosceles, here,
<TSR =<TRS = 40
Also the sum of angle in a triangle is 189, hence:
Arc SR+<TSR +<TRS = 18₩
ArcSR +40+40=180
ArcSR +80=180
ArcSR = 180-80
ArcSR = 100degrees
Hence the measure of SR is 100degrees
The measure of arc SR is 100°. The correct option is the third option - 100°
From the question, we are to determine the measure of arc SR.
The measure of arc SR = <STR
Now, we will determine the measure of <STR
In the diagram, T is the center of the circle.
∴ TP and TQ are radii.
Then, we can conclude that ΔPQT is an isosceles triangle.
Recall: Base angles of an isosceles triangle are equal.
∴ <PQT = <TPQ = 40°
Now, consider ΔPQT
<QTP + <TPQ + <PQT = 180° (Sum of angles in a triangle)
<QTP + 40° + 40° = 180°
<QTP + 80° = 180°
<QTP = 180° - 80°
<QTP = 100°
Also, in the diagram, <QTP and <STR are vertically opposite angles
NOTE: Vertically opposite angles are equal
That is, <QTP = <STR
∴ <STR = 100°
Hence, the measure of arc SR is 100°. The correct option is the third option 100°
Learn more on Calculating the measure of an arc here: https://brainly.com/question/3506007
Here is the complete and correct question:
Line PR and Line QS are diameters of circle T. What is the measure of Arc SR?
50°
80°
100°
120°
Please find the attached image
