What Is the Exterior Angle Theorem in Geometry?

TL;DR

The exterior angle theorem states that the exterior angle of a triangle is equal to the sum of its two remote interior angles. This theorem can be applied to find missing angles by using the relationship between the angles, with all angles in a triangle adding up to 180 degrees.

Transcript

in this lesson we're going to talk about the exterior angle theorem that is the exterior angle of a triangle is the sum of the two remote interior angles so let's use an example to illustrate this so here's a triangle let's do that again and let's say this angle is 40 and this angle is 60. what is the value of this angle now before we find the answ... Read More

Key Insights

• 🔺 The exterior angle of a triangle is equal to the sum of the two remote interior angles.
• 🔺 The sum of the angles in a triangle is always 180 degrees.
• 🪜 Linear pairs of angles add up to 180 degrees.
• 🔺 The exterior angle theorem can be used to calculate missing angles in a triangle.
• 🔺 Quadratic equations may be involved in solving for unknown angles.
• ☺️ Factoring quadratic equations is necessary to find the value of x in some cases.
• 🔺 The value of x can affect the values of multiple angles in a triangle.

Questions & Answers

Q: What is the exterior angle of a triangle?

The exterior angle of a triangle is equal to the sum of the two remote interior angles.

Q: How can we use the exterior angle theorem to calculate missing angles?

By knowing the value of one angle and using the exterior angle theorem, we can calculate the value of the unknown angle.

Q: What is the sum of the three angles in a triangle?

The sum of the three angles in a triangle is always 180 degrees.

Q: How do linear pairs of angles relate to the exterior angle theorem?

Linear pairs of angles always add up to 180 degrees, and this can be used in conjunction with the exterior angle theorem to calculate missing angles.

Summary & Key Takeaways

• The exterior angle of a triangle is the sum of the two remote interior angles.

• The three angles in a triangle always add up to 180 degrees.

• Linear pairs of angles add up to 180 degrees.