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Bisecting a Straight Angle

Part of the Angles section of Coddy's Geometry journey. Lesson 26 of 59.

A straight line is an angle too: the straight angle, 180°. Bisect it and each half is 90°, so the bisector of a straight angle stands perpendicular to the line. Two equal angles that fill a straight line are always right angles.

$A straight line with a ray making two angles marked equal$

The figure shows only matching arcs, no numbers. That is still enough: the two halves are equal and fill the line, so x + x = 180 and each is 90°. On the board, tap one half and pick Angles on a straight line: the arcs let the board share the 180° out.

A ray inside one of those right angles then splits a known 90°. If it makes 20° with the line, the other part is 70°.

Challenge

The ray OC bisects the straight angle AOB, and the ray OD sits inside ∠BOC. Find ∠DOC, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

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 Bisector Bisected ExpressionsBisecting a Straight AngleRecap: 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