Q. R The measure of arc PQ 2.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
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### Geometry Problem: Angle Measurement in a Circle

#### Diagram Description:
The diagram is composed of a circle intersected by three points labeled P, Q, and R forming an arc PQR. There is an angle marked as "2" at point R.

#### Problem Statement:
The measure of arc PQR is equal to 250 degrees. The measure of arc PR is equal to 110 degrees. What is the measure of angle 2?

#### Multiple Choice Answers:
- A) 125 degrees
- B) 70 degrees
- C) 180 degrees
- D) 55 degrees

#### Explanation of the Diagram:
The diagram shows:
- A circle with points P, Q, and R marked on its circumference.
- An arc PQR that covers a central angle.
- An angle at point R marked as "2".

#### Solution:

The measure of the remaining arc PSQ (which is 360 degrees minus arc PR) can be used to find angle 2.
This is calculated as follows:

Remaining arc = 360 degrees - (arc PR + arc PQR) 
              = 360 degrees - (110 degrees + 250 degrees) 
              = 360 degrees - 360 degrees 
              = 0 degrees

Since the arc PQ E is not zero, we should check:
Arc PQE is calculated from central angle
Central angle=0

Therefore, the correct answer is the measure of angle 2 is:
 - B) 70 degrees


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Transcribed Image Text:### Geometry Problem: Angle Measurement in a Circle #### Diagram Description: The diagram is composed of a circle intersected by three points labeled P, Q, and R forming an arc PQR. There is an angle marked as "2" at point R. #### Problem Statement: The measure of arc PQR is equal to 250 degrees. The measure of arc PR is equal to 110 degrees. What is the measure of angle 2? #### Multiple Choice Answers: - A) 125 degrees - B) 70 degrees - C) 180 degrees - D) 55 degrees #### Explanation of the Diagram: The diagram shows: - A circle with points P, Q, and R marked on its circumference. - An arc PQR that covers a central angle. - An angle at point R marked as "2". #### Solution: The measure of the remaining arc PSQ (which is 360 degrees minus arc PR) can be used to find angle 2. This is calculated as follows: Remaining arc = 360 degrees - (arc PR + arc PQR) = 360 degrees - (110 degrees + 250 degrees) = 360 degrees - 360 degrees = 0 degrees Since the arc PQ E is not zero, we should check: Arc PQE is calculated from central angle Central angle=0 Therefore, the correct answer is the measure of angle 2 is: - B) 70 degrees #### Navigation - [Previous](#)
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