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Solving with Verticals

Part of the Angles section of Coddy's Geometry journey. Lesson 16 of 59.

When both vertical angles carry a letter, the rule sets one label equal to the other. Now x appears on both sides of the equation, and you solve it as in Algebra: collect the x terms on one side and the numbers on the other.

$Two crossing lines with opposite angles 5x minus 12 and 3x plus 14 degrees$

Here the opposite angles are (5x - 12)° and (3x + 14)°, so $5x-12 = 3x+14$ . Take 3x from both sides: $2x-12 = 14$ . Add 12: $2x = 26$ , so $x = 13$ . Check: 5 × 13 - 12 = 53 and 3 × 13 + 14 = 53. The two angles match.

On the board, tap the two angles and pick Vertical angles. The board writes the equation for you.

Challenge

The lines PQ and RS cross at O. 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

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

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 EqualSolving with VerticalsAll 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 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