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Bisected Expressions

Part of the Angles section of Coddy's Geometry journey. Lesson 25 of 59.

When each half of a bisected angle carries an expression, the whole is twice that expression, parentheses and all. Two halves of (x + 12)° make 2(x + 12), not 2x + 12.

$A 70 degree angle bisected into two halves of x plus 12 degrees$

In the figure the whole is 70°, so $2\left(x+12\right) = 70$ . Divide both sides by 2 first: $x+12 = 35$ , so $x = 23$ . Check it: each half is 35°, and two of them are 70°.

On the board, tap a half and the whole, and pick Angle bisector. Dividing by 2 first keeps the numbers small.

Challenge

The ray BD bisects ∠ABC. Tap the angles you need, pick the rule that connects them, 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 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 BisectorBisected ExpressionsBisecting 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