Alternate angles - Examples, Exercises and Solutions

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.

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.

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.

Let's remember that adjacent angles are angles that are formed when two lines intersect each other.

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 each other to one hundred and eighty degrees, meaning their sum is 180 degrees. 

Let's remember that vertical angles are angles that are formed when two lines intersect, and they are created at the point of intersection, opposite each other.

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.

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.

Let's remember the definition of corresponding angles:

Corresponding angles are angles located on the same side of the line that cuts through the two parallels and are also situated at the same level with respect to the parallel line to which they are adjacent.

It seems that according to this definition these are the angles marked with the letter A.

Let's remember the definition of adjacent angles:

Adjacent angles are angles whose formation is possible in a situation where there are two lines that cross each other.

These angles are formed at the point where the intersection occurs, one next to the other, and hence their name.

Adjacent angles always complement each other to one hundred eighty degrees, that is, their sum is 180 degrees.

It seems that according to this definition these are the angles marked with the letter B.

Let's remember the different definitions of angles:

Corresponding angles are angles located on the same side of the line that intersects the two parallels and are also situated at the same level with respect to the parallel line they are adjacent to.

Therefore, according to this definition, these are the angles marked with the letter A

Alternate angles are angles located on two different sides of the line that intersects two parallels, and which are also not at the same level with respect to the parallel they are adjacent to.

Therefore, according to this definition, these are the angles marked with the letter B

Since we are given that ABCD is a trapezoid, lines AB and CD are parallel to each other.

Let's remember that alternate angles can be defined as a pair of angles that can be found in the opposite aspect of a line intended to intersect two parallel lines.

Additionally, these angles are positioned at opposite levels relative to the parallel line to which they belong.

Since in the given drawing we are told that the three lines are parallel to each other, we will remember that corresponding angles can be defined as a pair of angles that can be found on the same side of a line intended to intersect two parallel lines.

Additionally, these angles are located on the same level relative to the line they correspond to.

Since the angles are not on parallel lines, none of the answers are correct.

Since we are not given any information about the lines, we cannot define the lines as parallel.

As a result, none of the options are correct.

Given that line a is parallel to line b, let us remind ourselves of the definition of corresponding angles between parallel lines:

Corresponding angles are angles located on the same side of the line that intersects the two parallels and are also situated at the same level with respect to the parallel line to which they are adjacent.

Corresponding angles are equal in size.

According to this definition $\alpha=\beta$and as such they are the corresponding angles.

To solve the question, we must first remember that a parallelogram has two pairs of opposite sides that are parallel and equal.

That is, the top line is parallel to the bottom one.

From this, it is easy to identify that angle X is actually an alternate angle of angle δ, since both are on different sides of parallel straight lines.