SOLUTION: What is the measure of the angle formed by the bisectors of two angles of an equilateral triangle?

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Question 932490: What is the measure of the angle formed by the bisectors of two angles of an equilateral triangle?

Answer by MathLover1(20850) About Me  (Show Source):
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recall properties:
-The interior angles of a triangle always add up to 180
-Because the interior angles always add to 180°, every angle must be less than 180°
-The bisectors of the three interior angles meet at a point, called the in-center, which is the center of the in-circle of the triangle.
by definition an equilateral triangle is a triangle which has all three of its sides equal in length, and all three angles of an equilateral triangle are always 60°
in an equilateral triangle, the median, angle bisector, and altitude are equal also, they intersect at point G, the center of the inscribed and circumscribed circle
each of the angles are divided by the bisector (a line which cuts an angle into two equal halves ) in two angles of 30°
if the intersection of two bisectors is point G, and a triangle ABC,
a triangle formed by two bisectors and one side of triangle is AGB and angle AGB
so,the measure of the angle AGB is:
m < AGB=180-%2830%2B30%29=180-60=120°