Finding the Third Angle

Part of the Angles section of Coddy's Geometry journey. Lesson 43 of 62.

Add the three angle expressions and set their sum equal to 180°. Combine the known numbers, then solve for the unknown.

$A triangle with angles y plus 20, 75 and 45 degrees$

The triangle's angles satisfy (y + 20) + (75 + 45) = 180. Combine the constants to get y + 140 = 180, so y = 40. The labeled angle is then 60°, and 60 + 75 + 45 = 180 checks the total.

Challenge

Easy

The triangle’s angles are (x + 10)°, 55° and 60°.

$A triangle with angles x plus 10, 55 and 60 degrees$

Find x.

Try it yourself

(x + 10) + (55 + 60) = 180

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 Bisector Bisected Expressions Bisecting a Straight Angle Recap: Split in Half

9Triangle Angle Sum

The 180 RuleFinding the Third AngleTwo 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