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Four Angles, One Point

Part of the Angles section of Coddy's Geometry journey. Lesson 22 of 59.

With letters in the labels, the full turn gives an equation: every label, the square's 90 included, adds up to 360.

$Three angles around a point: 2x degrees, x plus 15 degrees and 105 degrees$

In the figure, $2x+\left(x+15\right)+105 = 360$ . Collect the x terms and the numbers: $3x+120 = 360$ , so $3x = 240$ and $x = 80$ . The angles are 160°, 95° and 105°, which do add up to 360.

On the board, tap the angles around the point and pick Angles around a point. If one carries a square, the board writes 90 for it.

Challenge

Four rays start at O. One angle carries a square and the others are labelled. Tap the angles, pick the rule, and solve the equation for x. Then press Check.

Try it yourself

$Use the figure to find x$

Use the figure to find 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 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 Point The Missing Angle Equal SlicesFour Angles, One PointRecap: 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