Exterior Angle Inequality

Learning Objectives Identify interior and exterior angles of a triangle. Distinguish between adjacent and remote interior angles relative to an exterior angle. State the Exterior Angle Inequality Theorem. Apply the Exterior Angle Inequality to compare angle measures in a triangle. Set up and solve simple one-variable inequalities based on the Exterior Angle Inequality. Use algebraic expressions to represent angle measures in inequality problems. Interpret solutions to inequalities in the context of angle measures. Have you ever wondered how we can compare the sizes of angles in a triangle without even measuring them? 🤔 It's like knowing one angle is definitely bigger than another just by looking at their positions! In this lesson, we'll discover a powerful rule...

TermDefinitionExample TriangleA polygon (a closed shape with straight sides) that has exactly three sides and three angles.A common shape you see everywhere, from pizza slices to road signs. Interior AngleAn angle formed inside a polygon by two adjacent sides.In a triangle ABC, angles ∠A, ∠B, and ∠C are the interior angles. Exterior AngleAn angle formed by one side of a polygon and the extension of an adjacent side.If you extend side BC of triangle ABC past C to point D, then ∠ACD is an exterior angle. Adjacent Interior AngleThe interior angle of a triangle that shares a vertex and a side with an exterior angle.For exterior angle ∠ACD, the adjacent interior angle is ∠ACB (which is also ∠C). Remote Interior AnglesThe two interior angles of a triangle that are not adjacent (not next to) a g...

Exterior Angle Inequality Theorem The measure of an exterior angle of a triangle is greater than the measure of either of its remote interior angles. $m\angle EXT > m\angle R_1$ $m\angle EXT > m\angle R_2$ This rule tells us that an exterior angle is always larger than each of the two interior angles that are not next to it. You use this to compare the sizes of angles directly. Exterior Angle Theorem (Sum of Remote Interior Angles) The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. $m\angle EXT = m\angle R_1 + m\angle R_2$ While the focus is on inequality, this theorem helps us understand *why* the inequality is true. Since $m\angle R_1$ and $m\angle R_2$ are positive, their sum ($m\angle EXT$) must...