Alternate interior angles are alternate angles located in the internal area between parallel lines. They are not on the same side of the transversal nor are they on the same level (floor) relative to the line.

Alternate interior angles are alternate angles located in the internal area between parallel lines. They are not on the same side of the transversal nor are they on the same level (floor) relative to the line.
Does the diagram show an adjacent angle?
In this article, we will learn about alternate interior angles, how to identify them, as well as their characteristics.
First, we need to remember what alternate angles are in general:
Alternate angles
Alternate angles between parallel lines are equal.
They are called alternate angles because they:
• Are not on the same side of the transversal line
• Are not on the same "level" relative to the line
Here are alternate angles for example:
The two marked angles are not on the same level and not on the same side, therefore they are alternate angles.
In order to confirm the presence of an alternate interior angle, you must observe that:
There is an exterior part - outside the two parallel lines
As well as an interior part - between the two parallel lines.
Let's examine the illustration:
In the illustration, we can see that the two alternate angles located between the two parallel lines in the inner part are alternate interior angles. Let's examine another example of a pair of alternate interior angles:
Note that in this illustration as well, you can observe that the two alternate angles are located in the internal part between the two parallel lines, and therefore they are alternate interior angles.
Bonus tip!
Alternate angles located in the external part outside the two parallel lines are called exterior alternate angles.
And now let's practice!
Here are two parallel lines and a line intersecting them.
a. Determine whether the angles shown are alternate angles.
b. Determine whether they are also alternate interior angles.
Solution:
a. Yes, the angles in the figure are alternate angles. They are not on the same side of the transversal and not on the same level relative to the line.
b. Yes, the alternate angles in the figure are interior since they are located in the inner part between the two parallel lines.
Another exercise:
Two parallel lines and a line intersecting them are shown.
a. Determine whether the angles shown are alternate angles
b. Determine whether they are alternate interior angles.
Solution:
a. Yes, the angles in the figure are alternate angles. They are not on the same level relative to the line and not on the same side of the transversal.
b. No. The angles are located in the external part outside the two parallel lines, therefore they are alternate angles but not interior ones.
Another exercise:
Here are two parallel lines and a line that intersects them.
Find the size of angle
and determine whether angle and angle are alternate interior angles.
Given that:
Solution:
According to the given information as well as the provided figue , we can determine that angle and angle are alternate angles. They are located between two parallel lines, each on a different side of the transversal and not on the same level relative to the line.
Alternate angles are equal to each other, therefore if we can conclude that angle
Additionally, we can also determine that the two angles are alternate interior angles because they are both located in the interior part between the two parallel lines.
Additional Exercise:
In all drawings, the two lines are parallel to each other.
a. Determine whether there are alternate interior angles in both drawings.
b. If in drawing the marked angle equals , what is angle ?
c. Determine true or false - only alternate exterior angles are equal to each other.
1.
2.
Solution:
a. No, only in the second drawing the two angles are alternate interior angles given that they are located in the inner part of the lines.
In the first drawing, the two angles are alternate exterior angles since they are located in the outer part of the lines.
b. The two angles marked in the drawing are alternate angles and therefore they are equal.
From this we can conclude that angle is also equal to .
C. Incorrect – exterior alternate angles are also equal to each other.
Does the diagram show an adjacent angle?
Does the diagram show an adjacent angle?
Does the diagram show an adjacent angle?
Does the diagram show an adjacent angle?
To determine if the diagram shows adjacent angles, we need to analyze the geometric arrangement shown:
In the diagram, both the vertical line and the diagonal line intersect at a point. This intersection point serves as the common vertex for the angles in question, as they radiate outward from this shared point.
Adjacent angles must share a common side or arm. In the diagram, the vertical line acts as one common side for both angles, with one angle extending upwards and the other horizontally from the vertex.
It is equally essential to ensure that these two angles do not overlap. Each angle branches from the vertex in a different direction, maintaining distinct interiors.
By confirming the presence of a common vertex and a common side without overlap of the angle interiors, the angles satisfy the definition of being adjacent.
Therefore, the diagram does indeed show adjacent angles.
Consequently, the correct answer is Yes.
Yes
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
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