Alternate Interior Angles Practice Problems & Solutions

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.

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.

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.

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.

To solve this problem, we will explore the concept of vertically opposite angles:

When two straight lines intersect each other at a point, they form two pairs of opposite angles. These pairs of angles are called vertically opposite angles.

The theorem of vertically opposite angles states that they are always equal to each other. Here's why:

• Consider two intersecting lines, forming four angles at their intersection point.
• These angles are labeled $\angle 1$, $\angle 2$, $\angle 3$, and $\angle 4$.
• The angles $\angle 1$ and $\angle 3$ are vertically opposite, as are $\angle 2$ and $\angle 4$.
• Since linear pairs of angles are supplementary, we have:
• $\angle 1 + \angle 2 = 180^\circ$
• $\angle 2 + \angle 3 = 180^\circ$
• From these equations, by setting the expressions for $\angle 2$ equal, we obtain that $\angle 1 = \angle 3$.
• Similarly, $\angle 2 = \angle 4$ by using the same reasoning.

Thus, it is established that vertically opposite angles are indeed equal.

Therefore, the statement "vertically opposite angles are equal to each other" is True.