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Four Angles, One Point

Part of the Angles section of Coddy's Geometry journey. Lesson 25 of 62.

More slices, same discipline. With several known angles and one unknown, resist touching the x until the knowns are gathered into a single number. One clean combine, one clean subtraction.

$Four angles around a point: 100, 105, 75 and y degrees$

In the figure: y + (100 + 105 + 75) = 360. The knowns gather: 100 + 105 + 75 makes 280, so y + 280 = 360 and y = 80. Three numbers or ten, the shape of the work stays two moves long.

Challenge

Medium

Four angles share the point: 130°, 95°, 85° and x°.

$Four angles around a point: 130, 95, 85 and x degrees$

Find x.

Try it yourself

x + (130 + 95 + 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 Point The Missing Angle Equal SlicesFour Angles, One PointRecap: 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