If one angles of triangle is 130 degree then the angle between the bis...
The sum of the angles in a triangle is always 180 degrees. Given that one angle of the triangle is 130 degrees, we can find the measure of the other two angles by subtracting 130 from 180.
- Angle 1: 130 degrees
- Angle 2: 180 - 130 = 50 degrees
- Angle 3: 180 - 130 = 50 degrees
Now, let's find the angle between the bisectors of the other two angles.
Finding the bisectors:
The bisector of an angle splits the angle into two equal parts. In a triangle, the angle bisector of an angle separates the opposite side into two segments that are proportional to the adjacent sides.
To find the angle bisectors, we need to use the angle bisector theorem. According to this theorem, the angle bisector of an angle in a triangle divides the opposite side into segments that are proportional to the adjacent sides.
Let's label the sides of the triangle:
- Side a is opposite to Angle 1 (130 degrees)
- Side b is opposite to Angle 2 (50 degrees)
- Side c is opposite to Angle 3 (50 degrees)
Now, let's find the angle bisectors using the angle bisector theorem:
- The angle bisector of Angle 2 divides side a into two segments that are proportional to sides b and c. Let's call the segments x and y.
- The angle bisector of Angle 3 divides side a into two segments that are proportional to sides b and c. Let's call the segments z and w.
By applying the angle bisector theorem, we have the following proportions:
- x/y = b/c
- z/w = b/c
Now, let's find the angle between the bisectors:
- The angle between the bisectors of Angle 2 and Angle 3 is equal to the difference between the angles formed by the bisectors with side a.
Let's call the angle between the bisectors as Angle A.
- Angle A = |(x/y) - (z/w)|
The value of Angle A depends on the values of x, y, z, and w, which in turn depend on the lengths of the sides of the triangle. Without knowing the lengths of the sides, we cannot determine the exact value of Angle A.
Therefore, we cannot choose any of the given options (50, 65, 90, or 155 degrees) as the correct answer. The angle between the bisectors can vary depending on the lengths of the sides of the triangle.
If one angles of triangle is 130 degree then the angle between the bis...
Question is from RS Aggarwal class 9. I didn't find any answer
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