Angles in Circles
Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.
Arcs in Circles
A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.
![### 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](#)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3cc721ad-58ca-43ac-b04d-0cef0046190e%2F4ff57f33-4743-4002-96c1-fd3d6bb02b23%2Fps2tz5m_processed.jpeg&w=3840&q=75)
![](/static/compass_v2/shared-icons/check-mark.png)
Step by step
Solved in 2 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
![Elementary Geometry for College Students](https://www.bartleby.com/isbn_cover_images/9781285195698/9781285195698_smallCoverImage.gif)
![Elementary Geometry For College Students, 7e](https://www.bartleby.com/isbn_cover_images/9781337614085/9781337614085_smallCoverImage.jpg)
![Elementary Geometry for College Students](https://www.bartleby.com/isbn_cover_images/9781285195698/9781285195698_smallCoverImage.gif)