find the unknown angles for the figure belowangle b=angle a= angle d=angle e=angle f=angle g=angle h= ### Transversals and Angle Relationships**Transversal and Angles Diagram**In the diagram shown:- Two parallel horizontal lines are intersected by a transversal, forming eight angles at the points of intersection.- The angles are labeled as follows: - At the upper intersection: $ a $, $ b $ as corresponding angles on the horizontal line, and $ d $ as the vertically opposite angle to $ b $. - At the lower intersection: $ e $, $ f $ as corresponding angles on the horizontal line, and $ g $ and $ h $ as related angles. The angle relationships provided are:- $ \angle a = 60^\circ $- $ \angle b = 4x - 30^\circ $### Analyzing Angle Relationships1. **Corresponding Angles**: Angles formed on the same side of a transversal with two parallel lines and are equal. - $ \angle a $ corresponds to $ \angle e $. - $ \angle b $ corresponds to $ \angle f $.2. **Alternate Interior Angles**: Angles formed on the opposite sides of a transversal but inside two parallel lines and are equal: - $ \angle d $ corresponds to $ \angle f $. - $ \angle e $ corresponds to $ \angle g $.3. **Alternate Exterior Angles**: Angles formed on the opposite sides of a transversal but outside two parallel lines and are equal: - $ \angle a $ corresponds to $ \angle h $. - $ \angle b $ corresponds to $ \angle g $.4. **Vertically Opposite Angles**: Angles directly opposite each other when two lines intersect and are always equal: - $ \angle b $ and $ \angle d $ are vertically opposite. - $ \angle f $ and $ \angle h $ are vertically opposite.### Solving for $ x $To find $ x $ using the given angle relationships:- Since $ \angle a $ and $ \angle b $ are corresponding angles and the lines are parallel:\[\angle a = \angle b\]Given:\[\angle a = 60^\circ\]\[\angle b = 4x - 30^\circ\]thus

b and 60 degrees are vertical angles. So they are equal. So, 4x-30=60 or, 4x=90 or, x=22.5

Answered: find the unknown angles for the figure…

Math

Geometry

find the unknown angles for the figure below angle b= angle a= angle d= angle e= angle f= angle g= angle h=

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter1: Line And Angle Relationships

Section1.4: Relationships: Perpendicular Lines

Problem 16E: Does the relation is less than for a numbers have a reflexive property consider one number? A...

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Concept explainers

Angles

In mathematics, angles constitute a very important part. Just like the concept of lines, an angle is a necessary figure that is used for measurement. How do you define its formation? It is formed when two or more lines meet at a point. The point at which two or more lines meet is known as the vertex. When the lines get inclined at this point, they do form various angles. Angles are measured from the vertex in terms of degrees.

Question

find the unknown angles for the figure below angle b= angle a= angle d= angle e= angle f= angle g= angle h=

### Transversals and Angle Relationships

**Transversal and Angles Diagram**

In the diagram shown:

- Two parallel horizontal lines are intersected by a transversal, forming eight angles at the points of intersection.
- The angles are labeled as follows:
- At the upper intersection: $ a $, $ b $ as corresponding angles on the horizontal line, and $ d $ as the vertically opposite angle to $ b $.
- At the lower intersection: $ e $, $ f $ as corresponding angles on the horizontal line, and $ g $ and $ h $ as related angles.

The angle relationships provided are:
- $ \angle a = 60^\circ $
- $ \angle b = 4x - 30^\circ $

### Analyzing Angle Relationships

1. **Corresponding Angles**: Angles formed on the same side of a transversal with two parallel lines and are equal.
- $ \angle a $ corresponds to $ \angle e $.
- $ \angle b $ corresponds to $ \angle f $.

2. **Alternate Interior Angles**: Angles formed on the opposite sides of a transversal but inside two parallel lines and are equal:
- $ \angle d $ corresponds to $ \angle f $.
- $ \angle e $ corresponds to $ \angle g $.

3. **Alternate Exterior Angles**: Angles formed on the opposite sides of a transversal but outside two parallel lines and are equal:
- $ \angle a $ corresponds to $ \angle h $.
- $ \angle b $ corresponds to $ \angle g $.

4. **Vertically Opposite Angles**: Angles directly opposite each other when two lines intersect and are always equal:
- $ \angle b $ and $ \angle d $ are vertically opposite.
- $ \angle f $ and $ \angle h $ are vertically opposite.

### Solving for $ x $

To find $ x $ using the given angle relationships:
- Since $ \angle a $ and $ \angle b $ are corresponding angles and the lines are parallel:
\[
\angle a = \angle b
\]
Given:
\[
\angle a = 60^\circ
\]
\[
\angle b = 4x - 30^\circ
\]
thus

Figure in plane geometry formed by two rays or lines that share a common endpoint, called the vertex. The angle is measured in degrees using a protractor. The different types of angles are acute, obtuse, right, straight, and reflex.

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