Question 179764
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I presume you mean that you need the measure of the angle formed by the intersection of the two bisectors of the other two angles in the triangle.

If one angle of a triangle measures 20 degrees, then the sum of the other two angles must be 180 - 20 = 160 degrees because the sum of the interior angles of a triangle is 180.

The bisectors of the other two angles form a triangle with vertices at the vertices of the two original bisected angles and the point of intersection of the bisectors.  Each of the angles at the original veritices is one-half of the orignial angle by definition of a bisector, so the sum of these two angles is one-half of the sum of the original angles previously determined to be 160 degrees, hence the sum of the half-angles is 80 degrees.

Again, since the sum of the measures of the interior angles of a triangle is 180 degrees, subtracting 80 leaves 100 degrees for the measure of the angle formed by the bisectors.

John
*[tex \LARGE e^{i\pi} + 1 = 0]
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