Alternate exterior angles are alternate angles located in the external part outside the parallel lines. Furthermore they are not on the same side of the transversal nor are they on the same level (floor) relative to the line.

Alternate exterior angles are alternate angles located in the external part outside the parallel lines. Furthermore they are not on the same side of the transversal nor are they on the same level (floor) relative to the line.
Identify the angle shown in the figure below?
Identify the angles shown in the diagram below?
Which type of angles are shown in the figure below?
Which type of angles are shown in the diagram?
\( a \) is parallel to
\( b \)
Determine which of the statements is correct.
Identify the angle shown in the figure below?
Remember that adjacent angles are angles that are formed when two lines intersect one another.
These angles are created at the point of intersection, one adjacent to the other, and that's where their name comes from.
Adjacent angles always complement one another to one hundred and eighty degrees, meaning their sum is 180 degrees.
Adjacent
Identify the angles shown in the diagram below?
Let's remember that vertical angles are angles that are formed when two lines intersect. They are are created at the point of intersection and are opposite each other.
Vertical
Which type of angles are shown in the figure below?
Alternate angles are a pair of angles that can be found on the opposite side of a line that cuts two parallel lines.
Furthermore, these angles are located on the opposite level of the corresponding line that they belong to.
Alternate
Which type of angles are shown in the diagram?
First let's remember that corresponding angles can be defined as a pair of angles that can be found on the same side of a transversal line that intersects two parallel lines.
Additionally, these angles are positioned at the same level relative to the parallel line to which they belong.
Corresponding
is parallel to
Determine which of the statements is correct.
Let's review the definition of adjacent angles:
Adjacent angles are angles formed where there are two straight lines that intersect. These angles are formed at the point where the intersection occurs, one next to the other, and hence their name.
Now let's review the definition of collateral angles:
Two angles formed when two or more parallel lines are intersected by a third line. The collateral angles are on the same side of the intersecting line and even are at different heights in relation to the parallel line to which they are adjacent.
Therefore, answer C is correct for this definition.
Colaterales Adjacent
If one of two corresponding angles is a right angle, then the other angle will also be a right angle.
If one vertically opposite angle is acute, then the other will be obtuse.
In which of the diagrams are the angles \( \alpha,\beta\text{ } \) vertically opposite?
If two adjacent angles are not right angles, then one of them is obtuse and the other is acute.
It is possible for two adjacent angles to be right angles.
If one of two corresponding angles is a right angle, then the other angle will also be a right angle.
To solve this problem, consider the following explanation:
When dealing with the concept of corresponding angles, we are typically considering two parallel lines cut by a transversal. The property of corresponding angles states that if two lines are parallel, then any pair of corresponding angles created where a transversal crosses these lines are equal.
Given the problem: If one of the corresponding angles is a right angle, we need to explore if this necessitates that the other corresponding angle is also a right angle.
Let’s proceed with the steps to solve the problem:
Therefore, based on the equality of corresponding angles when lines are parallel, if one corresponding angle is a right angle, the other angle will also be a right angle.
The final conclusion for the problem is that the statement is True.
True
If one vertically opposite angle is acute, then the other will be obtuse.
To solve this problem, we need to understand the properties of vertically opposite angles:
Given that vertically opposite angles are equal, if one angle is acute, the opposite angle must also be acute. This contradicts the statement in the problem that if one is acute, the other will be obtuse.
Therefore, the correct analysis of the problem reveals that the statement is incorrect.
Thus, the solution to the problem is False.
False
In which of the diagrams are the angles vertically opposite?
Remember the definition of angles opposite by the vertex:
Angles opposite by the vertex are angles whose formation is possible when two lines cross, and they are formed at the point of intersection, one facing the other. The acute angles are equal in size.
The drawing in answer A corresponds to this definition.
If two adjacent angles are not right angles, then one of them is obtuse and the other is acute.
To solve the problem, let’s consider the nature of adjacent angles:
Since both scenarios involve one angle being acute and the other obtuse, we verify that the statement is correct.
Therefore, the statement is true.
True
It is possible for two adjacent angles to be right angles.
To determine if it is possible for two adjacent angles to be right angles, we start by considering the definition of adjacent angles. Adjacent angles share a common side and a common vertex. We must think about this scenario in terms of the angles lying on a straight line or a flat plane.
A right angle is exactly . Hence, if we have two right angles that are adjacent, their measures would be:
When these two angles are adjacent, as defined in the problem, their sum is:
Angles that are adjacent along a straight line add up exactly to . Therefore, it is indeed possible for two adjacent angles to be both . This configuration simply means that these two angles lie along a straight line, dividing it into two right angles.
Hence, the statement is True.
True
It is possible for two adjacent angles to be obtuse.
Is it possible to have two adjacent angles, one of which is obtuse and the other right?
Does the diagram show an adjacent angle?
Does the diagram show an adjacent angle?
The sum of adjacent angles is 180 degrees.
It is possible for two adjacent angles to be obtuse.
To determine if two adjacent angles can both be obtuse, we first need to recall the definition of an obtuse angle and what it means for angles to be adjacent.
For two angles to both be obtuse, each must measure more than . Let's consider two angles, and , that are adjacent and both obtuse:
Adding both inequalities gives:
This sum would contradict the requirement that adjacent angles forming a linear pair sum to exactly .
Therefore, two adjacent angles cannot both be obtuse, as their sums would exceed the allowable amount for a linear pair.
Thus, it is not possible for two adjacent angles to be obtuse. The correct answer is False.
False
Is it possible to have two adjacent angles, one of which is obtuse and the other right?
Remember the definition of adjacent angles:
Adjacent angles always complement each other up to one hundred eighty degrees, that is, their sum is 180 degrees.
This situation is impossible since a right angle equals 90 degrees, an obtuse angle is greater than 90 degrees.
Therefore, together their sum will be greater than 180 degrees.
No
Does the diagram show an adjacent angle?
To determine whether the diagram shows adjacent angles, we need to confirm the presence of two properties:
1. Two angles must share a common vertex.
2. These angles must have a common arm and should not overlap.
Based on the given representation, the provided diagram consists solely of a single line. There are no visible intersecting lines or vertices from which angles can originate. Without intersection, there cannot be distinct angles, and thereby no adjacent angles can be identified.
Therefore, the diagram lacks the necessary properties to demonstrate adjacent angles. Hence, the correct choice is No.
No
Does the diagram show an adjacent angle?
To solve this problem, we'll follow these steps:
Now, let's work through each step:
Step 1: Inspecting the diagram, we notice several intersecting lines.
Step 2: To check for adjacent angles, we look for pairs of angles that share both a common vertex and a common side. An adjacent angle must be formed by such pairs, ensuring they do not overlap.
Step 3: Based on our definition, after closely examining the diagram, no pair of angles in the diagram seems to satisfy the definition of adjacent angles. The intersecting lines form angles that don't share a common arm with any other angle at the same vertex in the manner required for adjacency.
Therefore, the solution to the problem is No, the diagram does not show an adjacent angle.
No
The sum of adjacent angles is 180 degrees.
To solve this problem, let's first understand the concept of adjacent angles. Adjacent angles share a common vertex and a common side. When two adjacent angles are formed by two intersecting lines, they often form what is known as a linear pair.
According to the Linear Pair Postulate, if two angles form a linear pair, then the sum of these adjacent angles is degrees. This is because these angles lie on a straight line, effectively forming a straight angle, which measures degrees.
Let's apply this knowledge to the statement in the problem:
The statement says, "The sum of adjacent angles is 180 degrees." In the context of the Linear Pair Postulate, this is indeed correct as adjacent angles that create a linear pair sum to degrees.
Therefore, when the statement refers specifically to linear pairs, it is true.
Thus, the solution to the problem is True.
True