Triangle Angle-Sum Theorem

Learning Objectives Identify the three interior angles of any triangle. State the Triangle Angle-Sum Theorem accurately. Explain why the sum of the angles in a triangle is always 180 degrees. Apply the Triangle Angle-Sum Theorem to find a missing angle in a triangle when two angles are known. Solve simple problems involving the angles of a triangle. Recognize how the theorem applies to different types of triangles (e.g., right, acute, obtuse). Have you ever wondered why a triangular slice of pizza always seems to fit perfectly in your hand? 🍕 Or how builders make sure walls meet at just the right angles? Today, we'll discover a secret rule about triangles! In this lesson, you'll learn a fundamental rule about the angles inside any triangle, called the Triangle An...

TermDefinitionExample TriangleA polygon (a closed shape) with three straight sides and three interior angles.A slice of pizza, a yield sign, a musical triangle instrument. Vertex (plural: Vertices)A corner point of a triangle where two sides meet.Each of the three pointy parts of a triangle is a vertex. Interior AngleAn angle formed inside a triangle by two of its sides.The angles you measure at each vertex of a triangle are its interior angles. Degree (°)The unit used to measure angles. A full circle is 360 degrees.A right angle measures 90°. Right AngleAn angle that measures exactly 90°. It is often marked with a small square symbol.The corner of a square or a book, or the angle where a wall meets the floor. Acute AngleAn angle that measures less than 90°.The angle at the tip of a sharp...

Triangle Angle-Sum Theorem $\angle A + \angle B + \angle C = 180^\circ$ The sum of the measures of the three interior angles of any triangle is always 180 degrees. This rule applies to all triangles, no matter their size or shape. Finding a Missing Angle in a Triangle Missing Angle $= 180^\circ - (\text{Known Angle 1} + \text{Known Angle 2})$ If you know the measures of two angles in a triangle, you can find the measure of the third angle by adding the two known angles and subtracting their sum from 180 degrees.