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Vertical Angles Are Equal

Part of the Angles section of Coddy's Geometry journey. Lesson 18 of 62.

Now take two angles at the crossing that sit opposite each other, tip to tip. These are vertical angles, and they are always equal. Why: each one makes a linear pair with the same neighbor, so each equals 180° minus that neighbor. Same subtraction, same result.

$Two crossing lines with opposite angles 55 degrees and y degrees$

In the figure, y° sits opposite 55°, so y = 55 with no arithmetic at all. Vertical angles are the crossing’s gift: one measurement, and the opposite corner comes free.

Challenge

Easy

The two marked angles sit opposite each other at the crossing: (x + 25)° and 65°.

$Two crossing lines with opposite angles x plus 25 degrees and 65 degrees$

Find x.

Try it yourself

x + 25 = 65

Solve for 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 Naming Angles Adding Adjacent Angles Degrees and the Full Turn Acute, Right, Obtuse Recap: Adjacent Angles

4Vertical Angles

Linear PairsVertical Angles Are EqualSolving with Verticals All Four Angles Recap: At the Crossing

7Crossing Parallel Lines

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

10Isosceles Triangles

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

2Straight Lines and Supplements

Angles on a Line Supplementary Angles Three Angles on a Line 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

8Transversal Problems

Both Angles Labeled Verticals Meet Parallels From Figure to Equation Alternate with Algebra 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

Complementary Angles Finding the Complement Perpendicular Lines 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