In isosceles triangle ABC (where AB = BC), point E lies on AB and point D lies on BC. Given that angle B is 20 degrees, angle DAC is 60 degrees, and angle ACE is 50 degrees, find the measure of angle ADE. See also: HTML5 version

Adventitious angles,

Deceivingly difficult,

Langley's problem waits.

The famous **Langley problem** is a type of problem called "*Adventitious
Angles*" problem because it is a matter of chance that we will be
able to solve this problem (drawing auxiliary lines). It appears to be an easy problem, but it
is deceivingly difficult.

- Reference: The Mathematical Gazette, UK
- Author: Edward M. Langley
- Title: A problem
- Page: 173
- Issue: October 1922
- Category: M Note 644

See also:

Geometry

Dynamic Geometry

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Isosceles Triangle 80-20-80

Artwork of Langley's problem

Jigsaw Puzzle: Langley's Problem: 40 Quadrilateral Pieces

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40 Quadrilateral Pieces.

Over 1500 Visually Stimulating Geometry Problems.

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