Menu

From Figure to Equation

Part of the Angles section of Coddy's Geometry journey. Lesson 36 of 59.

Parallel lines with letters in the labels give equations, exactly as the straight line and the crossing did. Name the pair first, then let its rule decide the equation: equal for corresponding and alternate, adding to 180 for co-interior.

$Parallel lines and a transversal: corresponding angles x plus 15 degrees and 65 degrees$

Here (x + 15)° and 65° are in the same position at the two crossings: corresponding, so $x+15 = 65$ and $x = 50$ . Had they been co-interior, the equation would have been $\left(x+15\right)+65 = 180$ instead, with a different answer. Naming the pair is the step that decides.

On the board, tap the two angles and pick the rule. A wrong rule is refused with a reason, and that refusal tells you which pair it is not.

Challenge

AB ∥ CD, cut by the transversal GH. Tap the two labelled angles, pick the rule that connects them, and solve the equation for x. Then press Check.

Try it yourself

$Use the figure to find x$

Use the figure to find x

All lessons in Angles

1Meet the Angle

Your First Angle Angles on a Line Degrees and the Full Turn Across the Crossing

4Vertical Angles

Two Lines Cross Vertical Angles Are Equal Solving with Verticals All Four Angles Recap: At the Crossing

7Parallels and Transversals

Parallel Lines Corresponding Angles Alternate Angles Co-interior Angles Which Rule Is It Recap: The Three Pairs

10Isosceles and Equilateral

Base Angles Are Equal Finding the Apex Which Angles Match Equilateral Angles Isosceles at Work Recap: Twin Corners

2Naming and Equations

Adding Adjacent Angles Write the Equation Recap: Along the Line

5Around a Point

Angles Around a Point The Missing Angle Equal Slices Four Angles, One Point Recap: The Full Turn

8Angle Chases

Verticals Meet Parallels Is There Enough?From Figure to EquationBoth Angles Labeled Recap: Through the Strip

11The Exterior Angle

The Exterior Angle Using the Shortcut Two Roads, One Answer Exterior in the Wild Recap: Outside View

3Right Angles and Complements

The Square Mark Complementary Angles Perpendicular Lines Finding the Complement Equal Parts of a Corner Recap: The Right Corner

6The Angle Bisector

The Angle Bisector Bisected Expressions Bisecting a Straight Angle Recap: Split in Half

9Triangle Angle Sum

The 180 Rule Finding the Third Angle Two Unknown Angles Right Triangles Recap: The Budget

12Final Challenges

Final: The Angle Chase Final: Triangle Meets Line Final: The Full Round Final: Isosceles Chase Final: Master of Angles