Unknown Angles Equations

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Date:

🎯 WALT: Solve for unknown angles using multi-step equations

Success Criteria:

✓ I can identify angle relationships in diagrams

✓ I can set up algebraic equations from angle relationships

✓ I can solve multi-step equations to find unknown angles

✓ I can explain my reasoning using mathematical vocabulary

📐 Part 1: Angle Relationships

1. Two angles on a straight line have measures 3x and x + 20°. What is the value of x?

Remember: Angles on a straight line sum to 180°

2. Vertically opposite angles are marked as 2y - 15° and y + 30°. Find the value of y.

Remember: Vertically opposite angles are equal

3. Complementary angles are given as 4a and 2a + 6°. What is the measure of each angle?

Remember: Complementary angles sum to 90°

4. Four angles around a point are: x°, 2x°, (x + 30)°, and 90°. Find x.

Remember: Angles around a point sum to 360°

🧮 Part 2: Problem Solving with Diagrams

5. In the diagram below, find the value of x and then calculate all angle measures.

Two intersecting lines create four angles: (3x + 10)°, (5x - 30)°, and two others.

6. Supplementary angles are marked as (2x + 15)° and (3x - 35)°. Show your working to find x, then state both angle measures.

7. Three angles on a straight line are: x°, (2x + 10)°, and (x - 30)°. Find the value of x and verify your answer.

🚀 Extension Challenge

8. Advanced Problem: Two supplementary angles are expressed as 3(x + 5)° and 2(2x - 10)°. Use the distributive property to expand, then solve for x.

9. Create Your Own: Draw a diagram showing two intersecting lines. Label the angles using algebraic expressions with a variable. Write an equation and solve it.

10. Explain Your Thinking: How do you know when to use addition (angles on a line/around a point) versus setting expressions equal (vertically opposite angles)? Give an example of each.