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All Four Angles

Part of the Angles section of Coddy's Geometry journey. Lesson 20 of 62.

The crossing’s two rules work as a team. Opposite angles copy each other, and neighbors add to 180°. Know one angle, and all four fall: the opposite is a copy, and the two neighbors are its supplement.

$A crossing with all four angles marked: 55, 125, 55 and 125 degrees$

One measured 55° fills the figure: opposite 55°, neighbors 180 - 55 which is 125° each. The four always come as two matched couples, and the couples always add to 180° with each other. Check the total: 55 + 125 + 55 + 125 is 360, the full turn around the crossing point.

With labels the same rules write an equation. Neighbors of 2y° and (y + 60)° form a linear pair: 2y + (y + 60) = 180. Two y’s and one more y are three y’s, so 3y + 60 = 180, 3y = 120, and y = 40: the neighbors are 80° and 100°, and the other two copy them.

Challenge

Medium

At the crossing, the marked neighbors measure 2x° and (x + 30)°.

$Two crossing lines with neighboring angles 2x and x plus 30 degrees$

Find x.

Try it yourself

2x + (x + 30) = 180

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 Pairs Vertical Angles Are Equal Solving with VerticalsAll Four AnglesRecap: 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