If one of the angles of a triangle is 110°, then the angle between the bisectors of the other two angles is
a. 70°
b. 110°
c. 35°
d. 145°
Solution:
Given, one of the angles of a triangle is 110°.
We have to find the angle between the bisectors of the other two angles.
Consider a triangle ABC,
Let ∠A = 110°
By angle sum property of a triangle,
We know that the sum of all the three interior angles of the triangle is equal to 180 degrees.
So, ∠A + ∠B + ∠C = 180°
110° + ∠B + ∠C = 180°
∠B + ∠C = 180° - 110°
∠B + ∠C = 70°
Dividing by 2 on both sides,
∠B/2 + ∠C/2 = 70°/2
Now, 1/2(∠B + ∠C) = 35° --------------------- (1)
Considering triangle BOC,
By angle sum property of a triangle,
∠OBC + ∠OCB + ∠BOC = 180°
From (1),
∠BOC + 1/2(∠B + ∠C) = 180°
∠BOC + 35° = 180°
∠BOC = 180° - 35°
∠BOC = 145°
Therefore, the required angle is 145°.
✦ Try This: If one of the angles of a right angled triangle is 50°, then the other angle is equal to
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 27
If one of the angles of a triangle is 110°, then the angle between the bisectors of the other two angles is: a. 70°, b. 110°, c. 35°, d. 145°
Summary:
If one of the angles of a triangle is 110°, then the angle between the bisectors of the other two angles is 145°
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