Angles in Parallel Lines Practice Problems & Solutions

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:

• Step 1: Recognize that we are discussing corresponding angles formed by a transversal cutting through two parallel lines.
• Step 2: Apply the property that corresponding angles are equal when lines are parallel. This means if one angle in such a pair is a right angle, then the other must be equal to it.
• Step 3: Since a right angle measures $90^\circ$, the other corresponding angle must also measure $90^\circ$ since they are equal by the property of corresponding angles.

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.

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 $90^\circ$. Hence, if we have two right angles that are adjacent, their measures would be:

• First angle: $90^\circ$
• Second angle: $90^\circ$

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 $180^\circ$. Therefore, it is indeed possible for two adjacent angles to be both $90^\circ$. This configuration simply means that these two angles lie along a straight line, dividing it into two right angles.

Hence, the statement is True.

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 $180$ degrees. This is because these angles lie on a straight line, effectively forming a straight angle, which measures $180$ 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 $180$ degrees.

Therefore, when the statement refers specifically to linear pairs, it is true.

Thus, the solution to the problem is True.

To solve this problem, we need to understand the properties of vertically opposite angles:

• Vertically opposite angles are the angles that are opposite each other when two lines intersect.
• One key property of vertically opposite angles is that they are always equal in measure.
• An acute angle is defined as an angle that is less than $90^\circ$.
• An obtuse angle is defined as an angle that is greater than $90^\circ$.

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.

Adjacent angles are angles whose sum together is 180 degrees.

In the attached drawing, it is evident that there is no angle of 180 degrees, and no pair of angles can create such a situation.

Therefore, in the drawing there are no adjacent angles.