Drag the correct symbols into each box to create an expression for the measure, in degrees, of <XYZ, ### Angle Measurement in a CircleIn the given diagram, we see a circle with center $ O $ and an angle $ \angle XYZ $ inscribed in the circle. The circle also includes points $ X $, $ Y $, and $ Z $. The task is to determine the measure, in degrees, of $ \angle XYZ $ by creating an expression using the provided symbols.#### Step-by-Step Explanation:1. **Understanding the Diagram**: - **Diagram Description**: - Point $ O $ is the center of the circle. - $ XYZ $ is an inscribed angle in the circle. - $ k^\circ $ represents the angle at point $ X $ from the center $ O $ to point $ Z $.2. **Objective**: - To find the measure of $ \angle XYZ $, an expression needs to be constructed using the choices provided.3. **Given Choices**: - **Symbols provided** for creating the expression are: - Numbers: $ 90 $, $ 180 $ - Operations: $ + $, $ - $ - Variables: $ \frac{1}{2}k $, $ k $, $ 2k $4. **Drag and Drop Boxes**: - There are three boxes labeled $ 1 $, $ 2 $, and $ 3 $ where the correct symbols need to be placed to form the correct expression.#### Construction of the Expression:To construct the expression, follow these steps:- $ \angle XYZ $ is an inscribed angle, and inscribed angles subtended by the same arc are half the measure of the central angle subtending the same arc.- Given $ k^\circ $ is the central angle at $ O $, the inscribed angle $ \angle XYZ $ is half of $ k $.Thus, the correct expression for $ \angle XYZ $ is:1. Box 1: $ \frac{1}{2} k $2. Box 2: (Empty, since only one element is needed)3. Box 3: (Empty, since only one element is needed)Hence, filling in just the first box with $ \frac{1}{2} k $ would provide the appropriate measure for $ \angle XYZ $.By understanding the relationship between central angles and inscribed angles

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Description: Drag the correct symbols into each box to create an expression for the measure, in degrees, of <XYZ, ### Angle Measurement in a CircleIn the given diagram, we see a circle with center $ O $ and an angle $ \angle XYZ $ inscribed in the circle. The

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Answered: Drag the correct symbols into each box…

Math

Geometry

Drag the correct symbols into each box to create an expression for the measure, in degrees, of ZXY Z. 1 2 3

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

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.

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Question

Drag the correct symbols into each box to create an expression for the measure, in degrees, of <XYZ,

### Angle Measurement in a Circle

In the given diagram, we see a circle with center $ O $ and an angle $ \angle XYZ $ inscribed in the circle. The circle also includes points $ X $, $ Y $, and $ Z $. The task is to determine the measure, in degrees, of $ \angle XYZ $ by creating an expression using the provided symbols.

#### Step-by-Step Explanation:

1. **Understanding the Diagram**:
- **Diagram Description**:
- Point $ O $ is the center of the circle.
- $ XYZ $ is an inscribed angle in the circle.
- $ k^\circ $ represents the angle at point $ X $ from the center $ O $ to point $ Z $.

2. **Objective**:
- To find the measure of $ \angle XYZ $, an expression needs to be constructed using the choices provided.

3. **Given Choices**:
- **Symbols provided** for creating the expression are:
- Numbers: $ 90 $, $ 180 $
- Operations: $ + $, $ - $
- Variables: $ \frac{1}{2}k $, $ k $, $ 2k $

4. **Drag and Drop Boxes**:
- There are three boxes labeled $ 1 $, $ 2 $, and $ 3 $ where the correct symbols need to be placed to form the correct expression.

#### Construction of the Expression:
To construct the expression, follow these steps:
- $ \angle XYZ $ is an inscribed angle, and inscribed angles subtended by the same arc are half the measure of the central angle subtending the same arc.
- Given $ k^\circ $ is the central angle at $ O $, the inscribed angle $ \angle XYZ $ is half of $ k $.

Thus, the correct expression for $ \angle XYZ $ is:

1. Box 1: $ \frac{1}{2} k $
2. Box 2: (Empty, since only one element is needed)
3. Box 3: (Empty, since only one element is needed)

Hence, filling in just the first box with $ \frac{1}{2} k $ would provide the appropriate measure for $ \angle XYZ $.

By understanding the relationship between central angles and inscribed angles

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