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Vertical Angles Are Equal

Part of the Angles section of Coddy's Geometry journey. Lesson 15 of 59.

Vertical angles are always equal, and the reason takes one line of algebra. Each of the two opposite angles makes a linear pair with the same neighbour, so each is 180° minus that neighbour. The same subtraction gives the same result.

$Two crossing lines: 70 degrees, its neighbour 110 degrees, and the opposite angle 70 degrees$

In the figure, the neighbour is 110°. The angle on one side of it is 180 - 110 = 70°, and the angle on the other side is 180 - 110 = 70° as well. So the two opposite angles match, and you never need the neighbour to say so.

On the board this is the rule Vertical angles: tap an angle whose opposite angle is known and pick it.

Challenge

The lines PQ and RS cross at O. Find the angle marked ?, 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 CrossVertical Angles Are EqualSolving 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 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