Find the value of X **Understanding Angles and Circles:**This diagram is a representation of how various angles relate to each other when a circle and lines intersect.**Diagram Breakdown:**1. **Circle and Intersection Points:** - The diagram features a circle with two intersecting lines passing through it. - These intersections form angles both inside and outside the circle.2. **Labeled Angles:** - Inside the circle, one of the angles created by the intersecting lines is labeled as 40°. - Outside the circle, on the left side, an external angle is labeled 85°. - On the right side of the circle, another external angle is labeled 110°. - The angle outside the circle at the bottom intersection point is labeled as $x°$. **Key Mathematics Concept:**When two lines intersect at a single point and form adjacent angles around a circle, these angles hold specific properties. Particularly:- The exterior angle is equal to the sum of the two non-adjacent interior angles. To solve for $ x $ in this diagram: - The exterior angles outside the circle (85° and 110°) add up to form a straight line = 195°. - To find $ x $, understand that the sum of the angles in a straight line is always 180°. The inside properties of circle intersection angles give way to calculating around the circle's surface.Educational websites can use such diagrams to help learners visualize the relationships between angles and circles, furthering understanding of essential geometric principles.

Name: Find the value of X **Understanding Angles and Circles:**This diagram
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Description: Find the value of X **Understanding Angles and Circles:**This diagram is a representation of how various angles relate to each other when a circle and lines intersect.**Diagram Breakdown:**1. **Circle and Intersection Points:** - The diagram featur

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Answered: 85° 40° 110°

Math

Geometry

85° 40° 110°

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

Problem 1CT

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Concept explainers

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.

Topic Video

Question

Find the value of X

**Understanding Angles and Circles:**

This diagram is a representation of how various angles relate to each other when a circle and lines intersect.

**Diagram Breakdown:**

1. **Circle and Intersection Points:**
- The diagram features a circle with two intersecting lines passing through it.
- These intersections form angles both inside and outside the circle.

2. **Labeled Angles:**
- Inside the circle, one of the angles created by the intersecting lines is labeled as 40°.
- Outside the circle, on the left side, an external angle is labeled 85°.
- On the right side of the circle, another external angle is labeled 110°.
- The angle outside the circle at the bottom intersection point is labeled as $x°$.

**Key Mathematics Concept:**

When two lines intersect at a single point and form adjacent angles around a circle, these angles hold specific properties. Particularly:

- The exterior angle is equal to the sum of the two non-adjacent interior angles.

To solve for $ x $ in this diagram:
- The exterior angles outside the circle (85° and 110°) add up to form a straight line = 195°.
- To find $ x $, understand that the sum of the angles in a straight line is always 180°. The inside properties of circle intersection angles give way to calculating around the circle's surface.

Educational websites can use such diagrams to help learners visualize the relationships between angles and circles, furthering understanding of essential geometric principles.

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$Angles, Arcs, and Chords and Tangents$

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