Exterior Angle Theorem

Learning Objectives Identify interior and exterior angles of a triangle. Explain the relationship between an interior angle and its adjacent exterior angle. State the Exterior Angle Theorem for triangles. Apply the Exterior Angle Theorem to calculate unknown exterior angles. Use the Exterior Angle Theorem to find unknown interior angles. Solve simple problems involving exterior angles of triangles. Ever wonder how architects design buildings with slanted roofs or how robots turn precisely? 🤔 Angles are everywhere, and today we'll discover a cool secret about angles outside a triangle! In this lesson, you'll learn about exterior angles of triangles and a powerful rule called the Exterior Angle Theorem. This theorem helps us find missing angles without measuring, m...

TermDefinitionExample PolygonA closed two-dimensional shape made of straight line segments.Squares, rectangles, and triangles are all examples of polygons. TriangleA polygon with exactly three sides and three interior angles.A slice of pizza or a yield sign are common examples of triangles. Interior AngleAn angle located inside a polygon, formed by two adjacent sides.In a triangle ABC, the angles at vertices A, B, and C are its interior angles. Exterior AngleAn angle formed by one side of a polygon and the extension of an adjacent side. It is always outside the polygon.If you extend side BC of triangle ABC past C, the angle formed with side AC is an exterior angle at vertex C. Adjacent AnglesTwo angles that share a common vertex and a common side, but do not overlap.An interior angle and...

Linear Pair Property \text{Interior Angle} + \text{Adjacent Exterior Angle} = 180^\circ An interior angle and its adjacent exterior angle at the same vertex always form a straight line. Because they form a straight line, their sum is always 180 degrees. Exterior Angle Theorem \text{Exterior Angle} = \text{Opposite Interior Angle 1} + \text{Opposite Interior Angle 2} The measure of an exterior angle of a triangle is equal to the sum of the measures of its two interior angles that are not adjacent (not next to) to it.