Unsolved Problem

Angie & Beth

Throughout the quarter, this problem has provoked much thought, paper throwing, and hair pulling. The problem considers special triangles.

Given an isosceles triangle as shown, find the measure of angle Z:

We were able to find the angles shown above with the use of properties of triangles and lines. Since there are 180 degrees in a triangle and a straight line, the above angle measurements were found.

The line segments were extended outside of the triangle, in the hopes of finding the measure of angle Z. To our dismay, these extensions were of no help.

After extending other lines and getting nowhere, we decided to try our luck with those handy systems of equations. We found ourselves going around in circles:

This did not look so bad. Four equations, four unknowns. No sweat. Ha!

We then tried to solve using methods of substitution:

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