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All Four Angles

Part of the Angles section of Coddy's Geometry journey. Lesson 17 of 59.

One labelled angle at a crossing is enough to find all four. Its opposite angle is equal to it, and each of its neighbours makes 180° with it.

$Two crossing lines with angles 40, 140, 40 and 140 degrees$

Start from 40° in the figure. The angle opposite is also 40°. The two neighbours are each 180 - 40 = 140°. Check the whole crossing: 40 + 140 + 40 + 140 = 360, a full turn, as it must be.

So a crossing has only two sizes in it, and they add up to 180°. Find each unknown with the rule that reaches it from what you already know: Vertical angles across the point, Angles on a straight line to a neighbour.

Challenge

The lines PQ and RS cross at O. One angle is 118°. Find the three angles marked ?, giving each 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 VerticalsAll Four AnglesRecap: 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