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Video: Same-Side Exterior Angles: Definition & Theorem



Many kinds of angles are formed by intersecting lines. In this lesson, you’ll learn the definition and theorem of same-side exterior angles. Then, take a brief quiz to check what you learned.

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Lesson Transcript

Instructor:
Mia Primas

Mia has taught math and science and has a Master’s Degree in Secondary Teaching.

Many kinds of angles are formed by intersecting lines. In this lesson, you’ll learn the definition and theorem of same-side exterior angles. Then, take a brief quiz to check what you learned.

What Are Same-Side 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 same-side exterior. Same-side 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 same-side exterior relationship. Angles b and d also have a same-side exterior relationship.

Theorem

Remember, when parallel lines are cut by a transversal line, same-side 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 same-side 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 same-side 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 same-side exterior angles. The theorem states that same-side 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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  • Triangles: Definition and Properties

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  • Complementary Angles: Definition, Theorem & Examples

    4:24

  • Consecutive Interior Angles: Definition & Theorem

    3:42

  • Exterior Angle Theorem: Definition & Formula

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  • Half Angle: Rule, Formula & Examples

  • Perfect Parabola: Definition & Explanation

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