How to Solve Supplementary Angles Word Problems for GED Math

Understanding Supplementary Angles

• 🎯 The problem involves two angles, X and Y, that are supplementary, meaning they add up to 180 degrees.
• 🔑 A key piece of information is that one angle is eight times larger than its supplement.

Setting Up the Equations

• 💡 To solve for two unknown angles, we need two equations.
• 1️⃣ The first equation comes from the definition of supplementary angles: X + Y = 180.
• 2️⃣ The second equation represents the relationship between the angles: If Y is the larger angle, then Y = 8X.

Solving the Problem

• 🧠 We can use substitution to solve the system of equations. Substitute 8X for Y in the first equation: X + 8X = 180.
• ⚡ Combining like terms gives us 9X = 180.
• 🧮 Dividing both sides by 9, we find that X = 20.
• 📈 The larger angle, Y, would be 8 * 20 = 160. Both angles add up to 180 (20 + 160 = 180).

Identifying the Smaller Angle

• ✅ The question asks for the measure of the smaller angle.
• 🏆 Comparing X (20) and Y (160), the smaller angle is 20 degrees.