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Video: SameSide Exterior Angles: Definition & Theorem
Many kinds of angles are formed by intersecting lines. In this lesson, you’ll learn the definition and theorem of sameside exterior angles. Then, take a brief quiz to check what you learned.
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Mia Primas
Mia has taught math and science and has a Master’s Degree in Secondary Teaching.
What Are SameSide Exterior Angles?
When two parallel lines are cut by a third intersecting line, called a transversal line, eight angles are formed. These angles form different relationships with each other, one of them being sameside exterior. Sameside tells us that both angles are on the same side of the transversal line, and exterior tells us that both angles are exterior, or outside, of the parallel lines.
Let’s think of the parallel lines as hamburger buns. If the angles are outside of the buns, they are exterior. If they are inside the buns, they would be considered interior. In the following figure, angles a, b, c, and d are exterior to the parallel lines.
In this figure, angles a and c are on the same side of the transversal line, so they have a sameside exterior relationship. Angles b and d also have a sameside exterior relationship.
Theorem
Remember, when parallel lines are cut by a transversal line, sameside exterior angles are formed, which are outside of the parallel lines and on the same side of the transversal line. The theorem states that when parallel lines are cut by a transversal line, the sameside exterior angles are supplementary. Supplementary angles have a sum of 180 degrees. This theorem becomes very helpful when we are trying to find the angle measurements in a figure, as in the following example.
Example
Lines l and m are parallel lines cut by transversal line t. If angle 1 is 123 degrees, what is the measurement of angle 7?
We can see that angles 1 and 7 are sameside exterior. According to the theorem, they are supplementary, meaning that their angles add up to 180 degrees. If angle 1 is 123 degrees, then angle 7 must be 180 – 123 = 57 degrees.
Lesson Summary
Let’s review. When parallel lines are intersected by a transversal line, special angle relationships are formed. Two angles that are exterior to the parallel lines and on the same side of the transversal line are called sameside exterior angles. The theorem states that sameside exterior angles are supplementary, meaning that they have a sum of 180 degrees. Understanding this special angle relationship becomes helpful when calculating the measurement of angles.
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High School Geometry: Tutoring Solution
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Ch 1. Foundations of Geometry: Tutoring…
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Foundations of Geometry: Tutoring Solution
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Logic in Mathematics: Tutoring Solution
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Introduction to Geometric Figures: Tutoring Solution
Ch 4. Properties of Triangles: Tutoring Solution
Area of Triangles and Rectangles
5:43
Perimeter of Triangles and Rectangles
8:54
How to Identify Similar Triangles
7:23
Angles and Triangles: Practice Problems
7:43
Triangles: Definition and Properties
4:30
Classifying Triangles by Angles and Sides
5:44
Interior and Exterior Angles of Triangles: Definition & Examples
5:25
Constructing the Median of a Triangle
4:47
Median, Altitude, and Angle Bisectors of a Triangle
4:50
Constructing Triangles: Types of Geometric Construction
5:59
Properties of Concurrent Lines in a Triangle
6:17
306090 Triangle: Theorem, Properties & Formula
5:46
454590 Triangle: Theorem, Rules & Formula
4:31
Complementary Angles: Definition, Theorem & Examples
4:24
Consecutive Interior Angles: Definition & Theorem
3:42
Exterior Angle Theorem: Definition & Formula
6:06
Half Angle: Rule, Formula & Examples
Perfect Parabola: Definition & Explanation
SameSide Exterior Angles: Definition & Theorem
2:44
3:17
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SameSide Interior Angles: Definition & Theorem
How to Find the Centroid of a Triangle
How to Find Amplitude of a Sine Function
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Properties of Triangles: Tutoring Solution
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