Finding the Third Angle

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

With an expression in one corner, the 180 budget becomes an equation: all three labels, added, equal 180. Gather the plain numbers first, as always.

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

In the figure, (y + 20) + (75 + 45) = 180. The numbers gather: 20 + 75 + 45 makes 140, so y + 140 = 180 and y = 40. The labeled corner is then 60°, and 60 + 75 + 45 spends the budget exactly.

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