Q. 50
If the vertical angle of a triangle is 130°, then the angle between the bisectors of the base angles of the triangle is
A. 65°
B. 100°
C. 130°
D. 155°
Answer :
Let x and y be the bisected angles.
So in the original triangle, sum of angles is
130 + 2x + 2y = 180
2(x + y) = 50
x + y= 25
In the smaller triangle consisting of the original side opposite 130 and the 2 bisectors,
x + y + Base Angle = 180
25 + Base Angle = 180
Base Angle = 155o
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