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The Missing Angle

Part of the Angles section of Coddy's Geometry journey. Lesson 20 of 59.

A full turn often hides one of its numbers in a square. The square is 90°, and it counts toward the 360° like any labelled angle. Forgetting it is the most common mistake here.

$Three angles around a point: a right angle with a square, 150 degrees and 120 degrees$

In the figure, the square angle is 90°, so 90 + 150 + 120 = 360. To find a missing angle in a turn like this, first turn the square into its number with Right angle, then use Angles around a point.

Challenge

Four rays start at O. One angle carries a square and two others are labelled. 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 Cross Vertical Angles Are Equal Solving 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 PointThe Missing AngleEqual 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