If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be
a) 50°
b) 65°
c) 145°
d) 155°
Solution:
Given, the measure of one of the angles of a triangle is 130°
We have to find the angle between the bisectors of the other two angles.
We know that the sum of all three interior angles of a triangle is always equal to 180 degrees.
Let us consider a triangle ABC
∠A + ∠B + ∠C = 180°
Given, ∠A = 130°
So, 130° + ∠B + ∠C = 180°
∠B + ∠C = 180° - 130°
∠B + ∠C = 50°
Dividing by 1/2 on both sides,
1/2∠B + 1/2∠C = 50/2°
∠B/2 + ∠C/2 = 25° ---------------- (1)
From the figure,
We observe that OB and OC are the angle bisectors of ∠ABC and ∠ACB.
Considering triangle OBC,
∠OBC + ∠OCB + ∠BOC = 180°
∠B/2 + ∠C/2 + ∠BOC = 180°
From (1),
25° + ∠BOC = 180°
∠BOC = 180° - 25°
∠BOC = 155°
Therefore, the angle between the angle bisectors of two angle is 155°
✦ Try This: If one of the angles of a triangle is 120°, then the angle between the bisectors of the other two angles can be
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 6
NCERT Exemplar Class 9 Maths Exercise 6.1 Problem 5
If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be a) 50°, b) 65°, c) 145°, d) 155°
Summary:
If one of the angles of a triangle is 130°, then the angle between the bisectors of the other two angles can be 155°
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