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Angles Around a Point

Part of the Angles section of Coddy's Geometry journey. Lesson 22 of 62.

Stand rays out from a single point in every direction and look at the angles between them. Together they sweep once around the point: a full turn. So angles around a point always add to 360°.

$Three angles around a point: 140, 130 and y degrees$

In the figure, y + (140 + 130) = 360. Combine the numbers: y + 270 = 360, so y = 90. The method never changes with the count: gather what is known, and the full turn pays out the rest.

Challenge

Easy

Three angles share the point in the figure: 160°, 85° and x°.

$Three angles around a point: 160, 85 and x degrees$

Find x.

Try it yourself

x + (160 + 85) = 360

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

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 PointThe 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