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Isosceles at Work

Part of the Angles section of Coddy's Geometry journey. Lesson 51 of 62.

Expressions join the symmetry. An isosceles triangle with a labeled apex still obeys both of its rules at once: base angles equal, budget 180. Read the ticks, copy the known base angle, and write the full sum.

$An isosceles triangle with apex y plus 15 degrees and base angles of 65 degrees$

In the figure the ticks double the 65°: (y + 15) + (65 + 65) = 180. Gather 145, so y + 145 = 180 and y = 35. The apex is then 50°, and 50 + 65 + 65 closes the budget exactly.

Challenge

Medium

The ticked triangle has apex (x + 20)° and base angles of 50° each.

$An isosceles triangle with apex x plus 20 degrees and base angles of 50 degrees$

Find x.

Try it yourself

(x + 20) + (50 + 50) = 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

1Meet the Angle

Your First Angle Naming Angles Adding Adjacent Angles Degrees and the Full Turn Acute, Right, Obtuse Recap: Adjacent Angles

4Vertical Angles

Linear Pairs Vertical Angles Are Equal Solving with Verticals All Four Angles Recap: At the Crossing

7Crossing Parallel Lines

Parallel Lines Corresponding Angles Alternate Angles Co-interior Angles Which Rule Is It Recap: The Three Pairs

10Isosceles Triangles

Base Angles Are Equal Finding the Apex Which Angles Match Equilateral AnglesIsosceles at WorkRecap: Twin Corners

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 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