Alternate exterior angles are alternate angles located in the external part outside the parallel lines. Furthermore they are not on the same side of the transversal nor are they on the same level (floor) relative to the line.
Alternate Exterior Angles Practice Problems & Solutions
Master alternate exterior angles with step-by-step practice problems. Learn to identify, calculate, and solve angle relationships in parallel lines.
📚Master Alternate Exterior Angles Through Interactive Practice
- Identify alternate exterior angles in parallel line diagrams with transversals
- Calculate missing angle measures using the alternate exterior angles theorem
- Distinguish between alternate exterior and alternate interior angle pairs
- Apply angle properties to solve real-world geometry problems
- Recognize when angles are equal using parallel line relationships
- Solve multi-step problems involving alternate exterior angles
Understanding Angles in Parallel Lines
Complete explanation with examples
Alternate exterior angles
Practice Angles in Parallel Lines
Test your knowledge with 48 quizzes
Does the diagram show an adjacent angle?
Examples with solutions for Angles in Parallel Lines
Step-by-step solutions included
Exercise #1
If one of two corresponding angles is a right angle, then the other angle will also be a right angle.
Step-by-Step Solution
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 , the other corresponding angle must also measure 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.
Answer:
True
Video Solution
Exercise #2
It is possible for two adjacent angles to be right angles.
Step-by-Step Solution
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:
- First angle:
- Second angle:
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.
Answer:
True
Video Solution
Exercise #3
The sum of adjacent angles is 180 degrees.
Step-by-Step Solution
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 degrees. This is because these angles lie on a straight line, effectively forming a straight angle, which measures 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 degrees.
Therefore, when the statement refers specifically to linear pairs, it is true.
Thus, the solution to the problem is True.
Answer:
True
Video Solution
Exercise #4
If one vertically opposite angle is acute, then the other will be obtuse.
Step-by-Step Solution
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 .
- An obtuse angle is defined as an angle that is greater than .
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.
Answer:
False
Video Solution
Exercise #5
Does the drawing show an adjacent angle?
Step-by-Step Solution
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.
Answer:
Not true
Video Solution
Frequently Asked Questions
What are alternate exterior angles in parallel lines?
+Alternate exterior angles are pairs of angles that lie outside two parallel lines on opposite sides of a transversal line. These angles are always equal when the lines are parallel and are located at different levels relative to the parallel lines.
How do you identify alternate exterior angles?
+To identify alternate exterior angles, look for: 1) Two angles outside the parallel lines, 2) Angles on opposite sides of the transversal, 3) Angles at different levels (not aligned horizontally). If all three conditions are met, the angles are alternate exterior angles.
Are alternate exterior angles always equal?
+Yes, alternate exterior angles are always equal when formed by parallel lines and a transversal. This is a fundamental theorem in geometry that helps solve many angle problems involving parallel lines.
What's the difference between alternate exterior and interior angles?
+The key difference is location: alternate exterior angles are outside the parallel lines, while alternate interior angles are between the parallel lines. Both types are equal to their corresponding alternate angle when lines are parallel.
How do you solve problems with alternate exterior angles?
+Follow these steps: 1) Identify the parallel lines and transversal, 2) Locate the alternate exterior angle pairs, 3) Set up equations using the fact that alternate exterior angles are equal, 4) Solve for unknown angle measures algebraically.
Do alternate exterior angles add up to 180 degrees?
+No, alternate exterior angles do not add up to 180 degrees - they are equal to each other. Angles that add up to 180 degrees are called supplementary angles, which is a different relationship than alternate angles.
Can you have alternate exterior angles without parallel lines?
+While you can have angles in similar positions without parallel lines, they won't be equal unless the lines are parallel. The equal relationship of alternate exterior angles is a property that only exists when the lines are truly parallel.
What grade level learns alternate exterior angles?
+Alternate exterior angles are typically taught in middle school geometry (grades 7-8) and reinforced in high school geometry courses. Students learn this concept alongside other parallel line angle relationships and basic geometric proofs.