If you know the measure of the vertex angle of an isosceles triangle, how do you find out the measure of the base angles?

Step-by-step explanation:

An isosceles triangle has 2 sides that are the same length.  Let's say that our triangle has the 2 sides measuring the same and the base is a different length.  The vertex angle is the top angle.  By the definition of an isosceles triangle, since the 2 sides measure the same length, then the angles across from those sides have the same degree measure.  If we know the measure of the vertex angle, then we have

180 = vertex angle - base angle - base angle

but since the base angles are the same and we have 2 of them, then

180 = vertex angle - 2 base angles

For example, if the vertex angle measures 80 degrees, then 180 - 80 = 100.  That 100 has to be split in half for each of the base angles which are the same as each other.  So the vertex angle is 80 and each base is 50.

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