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
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
Exercise #2
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
Exercise #3
Which type of angles are shown in the figure below?
Step-by-Step Solution
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.
Answer:
Alternate
Exercise #4
Which type of angles are shown in the diagram?
Step-by-Step Solution
First 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.
Answer:
Corresponding
Exercise #5
Identify the angles shown in the diagram below?
Step-by-Step Solution
Let's remember that vertical angles are angles that are formed when two lines intersect. They are are created at the point of intersection and are opposite each other.
Answer:
Vertical
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.