Alternate Interior Angles Practice Problems & Solutions

To solve this problem, we'll follow these steps:

• Step 1: Inspect the given diagram for angles.
• Step 2: Determine if any angles share a common vertex and a common side.
• Step 3: Verify that the angles do not overlap.

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.

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.

To determine if the diagram shows adjacent angles, we need to analyze the geometric arrangement shown:

• Step 1: Identify the common vertex.

  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.

• Step 2: Identify the common side.

  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.

• Step 3: Ensure no overlap of interiors.

  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.

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 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.