Solve a system of equations in three variables using substitution

Learning Objectives Identify a known angle value in a picture puzzle. Explain that different shapes can represent unknown angle measures. Use the 'substitution' or 'swap' method to replace a shape with its known number value in a simple angle equation. Solve for a single unknown angle measure using basic addition and subtraction. Find the values of three unknown angles by solving a series of related picture puzzles. Check their answers by putting their final angle values back into the original puzzles. Ready to be an Angle Detective? 🕵️‍♀️ We have a mystery where the sizes of some angles are missing, and we need your help to find them! In this lesson, we will learn how to solve angle puzzles that have three different mystery angles. We'll use a spec...

TermDefinitionExample Unknown AngleAn angle in our puzzle whose size in degrees we don't know yet. We will use fun shapes like a square (■), a circle (●), and a triangle (▲) to represent these unknowns.In the puzzle '■ + 20° = 90°', the square shape (■) is the unknown angle. Known ValueA number or angle size that is given to us in the puzzle. This is our first clue!If a puzzle tells you 'The triangle angle ▲ is 30°,' then 30° is a known value. System of Angle PuzzlesA group of two or more angle puzzles that are connected. The shapes (■, ●, ▲) mean the same thing in all the puzzles in the group. You have to use clues from one puzzle to help solve another.Puzzle 1: ■ + ● = 100°. Puzzle 2: ■ = 40°. These two puzzles make a system because the ■ is the same in both. Su...

Angles on a Straight Line Angle_{1} + Angle_{2} + ... = 180° When several angles are next to each other and form a straight line, all their measures add up to 180°. We can use this to build a puzzle. Angles in a Right Angle Angle_{1} + Angle_{2} + ... = 90° When smaller angles fit together to form a perfect corner (a right angle), their measures must add up to 90°. Angles in a Triangle Angle_{A} + Angle_{B} + Angle_{C} = 180° The three inside angles of any triangle always add up to 180°. This is a very helpful rule for our puzzles.