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Bisected Expressions

Part of the Angles section of Coddy's Geometry journey. Lesson 28 of 62.

When each half of a bisected angle carries an expression, the doubling wraps the whole expression: two parts of (y + 5)° make 2(y + 5) in total, parentheses and all.

$A 50 degree angle bisected into two equal parts of y plus 5 degrees$

The figure’s whole is 50°, so 2(y + 5) = 50. Divide both sides by 2 first: y + 5 = 25, and y = 20. Each half is then 25°, and two of them rebuild the 50. Dividing before expanding keeps the numbers small: the parenthesis was built to be undone.

Challenge

Medium

The bisected angle in the figure is a right angle: the square says 90°. Each half measures (x + 10)°.

$A right angle bisected into two equal parts of x plus 10 degrees$

Find x.

Try it yourself

2(x + 10) = 90

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 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 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