Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter4: Polynomials
Section4.6: Multiplying Polynomials
Problem 4OE
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Question
![**Problem Statement:**
Given the following circle, find the value of \( x \).
**Diagram Explanation:**
- The diagram shows a circle with some marked angles.
- There is a chord in the circle creating an angle of \( 145^\circ \) on the circumference.
- One of the angles inside the circle is marked as \( 85^\circ \) and another angle, subtended by the same chord but outside the circle is marked as \( 95^\circ \).
- The angle \( x \) is formed outside the circle where the two lines intersect forming an extended angle from inside the circle.
**Mathematical Details:**
- The exterior angle \( x \) is found by the relationship that the exterior angle is equal to the sum of the opposite interior angles.
**Steps to Solve:**
1. Identify that the external angle \( x \) at the point of intersection outside the circle is equal to the sum of the angles 145° (inside the circle) and 85° (inside the circle).
2. Apply the formula for the exterior angle of a circle:
\[ x = 85^\circ + 95^\circ \]
3. Calculate \( x \):
\[ x = 85^\circ + 95^\circ = 180^\circ \]
**Result:**
The value of \( x \) is \( 80^\circ \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa7c29d2f-5cf3-43f5-aa90-abc5a822140a%2Fbc4b0374-082b-4713-84d7-f84ae5831e49%2Fk5crigr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem Statement:**
Given the following circle, find the value of \( x \).
**Diagram Explanation:**
- The diagram shows a circle with some marked angles.
- There is a chord in the circle creating an angle of \( 145^\circ \) on the circumference.
- One of the angles inside the circle is marked as \( 85^\circ \) and another angle, subtended by the same chord but outside the circle is marked as \( 95^\circ \).
- The angle \( x \) is formed outside the circle where the two lines intersect forming an extended angle from inside the circle.
**Mathematical Details:**
- The exterior angle \( x \) is found by the relationship that the exterior angle is equal to the sum of the opposite interior angles.
**Steps to Solve:**
1. Identify that the external angle \( x \) at the point of intersection outside the circle is equal to the sum of the angles 145° (inside the circle) and 85° (inside the circle).
2. Apply the formula for the exterior angle of a circle:
\[ x = 85^\circ + 95^\circ \]
3. Calculate \( x \):
\[ x = 85^\circ + 95^\circ = 180^\circ \]
**Result:**
The value of \( x \) is \( 80^\circ \).
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