### Geometry Problem: Finding the Measure of Angle 5**Diagram Description:**The image displays a geometric diagram with two intersecting lines, forming various angles. More precisely, the intersecting lines create eight angles, labeled 1 through 9 as follows:- Angles 1, 2, and 3 are on the lower right side.- Angles 4, 5, and 6 are on the left side.- Angles 7, 8, and 9 are on the top right side.**Given Information:**- The measure of angle 7 ($ m/\angle 7 $) is $ 102^\circ $.- The measure of angle 2 ($ m/\angle 2 $) is $ 49^\circ $.**Problem:**Find the measure of angle 5 ($ m/\angle 5 $).**Solution Steps:**1. **Identify Vertical Angles:** - Angles 7 and 3 are vertical angles and are therefore equal. So, $ m/\angle 3 = 102^\circ $.2. **Identify Alternate Interior Angles:** - Angles 2 and 3 are on opposite sides of the transversal and are equal. - Since $ m/\angle 2 = 49^\circ $, and the lines present are parallel with 2 being the interior angle sharing a transversal with 3, angle 3 must also measure 49 degrees. 3. **Using the Angle Sum Property:** - Considering the straight line crossing through angles 4, 5, and 6, they must aggregate to $180^\circ $ (Supplementary angles). - Given: $ m/\angle 4 + m/\angle 5 + m/\angle 6 = 180^\circ $ - Also, angles 4 and 6 form linear pairs with 7 and 5 respectively: $ m/\angle 7 = 102^\circ \Rightarrow m/\angle 6 = 78^\circ $ (180 - 102) - As angles 4 and 6 are vertically opposite angles cutting 5, they are also equal (Linear angle sum property with right angles completing the shape as per transversal intersection). With: m/\|angle 8=\ ### Hence calculation verifies 49 Triangle angles and inner defining lines

Answered: Image /qna-images/answer/d9447546-ff71-4d32-8fa9-5536b4b001ae.jpg

Answered: 3) = 102° and m/2 = 49° find m/5

Math

Geometry

3) = 102° and m/2 = 49° find m/5

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

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A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.

Question

### Geometry Problem: Finding the Measure of Angle 5

**Diagram Description:**
The image displays a geometric diagram with two intersecting lines, forming various angles. More precisely, the intersecting lines create eight angles, labeled 1 through 9 as follows:

- Angles 1, 2, and 3 are on the lower right side.
- Angles 4, 5, and 6 are on the left side.
- Angles 7, 8, and 9 are on the top right side.

**Given Information:**
- The measure of angle 7 ($ m/\angle 7 $) is $ 102^\circ $.
- The measure of angle 2 ($ m/\angle 2 $) is $ 49^\circ $.

**Problem:**
Find the measure of angle 5 ($ m/\angle 5 $).

**Solution Steps:**
1. **Identify Vertical Angles:**
- Angles 7 and 3 are vertical angles and are therefore equal. So, $ m/\angle 3 = 102^\circ $.

2. **Identify Alternate Interior Angles:**
- Angles 2 and 3 are on opposite sides of the transversal and are equal.
- Since $ m/\angle 2 = 49^\circ $, and the lines present are parallel with 2 being the interior angle sharing a transversal with 3, angle 3 must also measure 49 degrees.

3. **Using the Angle Sum Property:**
- Considering the straight line crossing through angles 4, 5, and 6, they must aggregate to $180^\circ $ (Supplementary angles).
- Given:
$ m/\angle 4 + m/\angle 5 + m/\angle 6 = 180^\circ $
- Also, angles 4 and 6 form linear pairs with 7 and 5 respectively:
$ m/\angle 7 = 102^\circ \Rightarrow m/\angle 6 = 78^\circ $ (180 - 102)
- As angles 4 and 6 are vertically opposite angles cutting 5, they are also equal (Linear angle sum property with right angles completing the shape as per transversal intersection).

With:
m/\|angle 8=\

### Hence calculation verifies 49 Triangle angles and inner defining lines

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