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Verticals Meet Parallels

Part of the Angles section of Coddy's Geometry journey. Lesson 34 of 59.

Some pairs match none of the parallel rules. Then you chase: trade the angle you know for one that a rule links to the target. The trade is a rule you already have, a vertical angle or a neighbour on a straight line, and then one parallel rule finishes.

$Parallel lines and a transversal: 110 degrees above the top line, an unknown between the lines at the bottom crossing$

Here the 110° angle is outside the parallels and ? is inside, on the other side: not corresponding, not alternate, not co-interior. Its vertical angle, though, sits between the lines on the right of the transversal, and is 110° too. That angle and ? are co-interior, so ? = 180 - 110 = 70°.

Each step on the board is one tap and one rule. You choose which angle to find first, and any order that works is fine.

Challenge

AB ∥ CD, cut by the transversal GH. Find the angle marked ?, giving every step its rule, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

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 ParallelsIs There Enough?From Figure to Equation Both 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