# Geometry Problem 1529: Unlock the Mystery of Triangles: Solving for the Missing Angle with 100-50-30 Degree Angles and Cevian Lengths - A High School Challenge

In a triangle ABC, angle A measures 30 degrees, angle C measures 100 degrees. BD is an interior cevian such that BD is equal to AC. Calculate the measure of angle
BDC.

## Discover Even More: See Also...

### Problem 1530

### Problem 1528

### Problem 1527

### Problem 1526

### Problem 1525

### Problem 1524

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Thematic Poem:

Unraveling the Secrets of a Mysterious Triangle

Amidst the angles sharp and bold,

A triangle with
secrets untold,

Degrees of 100, 50, and 30,

A
riddle waiting to ensue.

But as we search, we may discover,

A shape with
sides so equal in measure,

An equilateral, hidden
within,

A hint to the mystery therein.

And as we ponder, with our minds so bright,

An
auxiliary line may come in sight,

A tool to unlock
the triangle's hold,

And reveal its secrets, pure as
gold.

And lo and behold, what do we see?

An isosceles
triangle, waiting to be set free,

With sides and
angles that match so fine,

A missing angle, no longer
left behind.

So let us solve this puzzle, with grace and wit,

And uncover the mysteries, bit by bit,

With
equilateral, auxiliary, and isosceles,

Our journey
ends in triumph, oh so seamless.

If you're interested in finding more poems with a
focus on geometry, you may enjoy this collection:
More geometry thematic poems.

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