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Both Angles Labeled

Part of the Angles section of Coddy's Geometry journey. Lesson 37 of 59.

When both angles carry a letter, the rule works the same way. For an equal pair, set the labels equal and collect x on one side. For co-interior angles, add the labels, brackets and all, and set the sum to 180.

$Co-interior angles: x plus 20 degrees and 2x plus 40 degrees$

Here (x + 20)° and (2x + 40)° are co-interior, so $\left(x+20\right)+\left(2x+40\right) = 180$ . Collect: $3x+60 = 180$ , so $3x = 120$ and $x = 40$ . The angles are 60° and 120°, which add to 180 as they should.

Challenge

AB ∥ CD, cut by the transversal GH. Both marked angles carry x. Tap them, pick the rule, and solve 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 EquationBoth Angles LabeledRecap: 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