In ∆ABC, if ∠A = ∠C, and exterior angle ABX = 140°, then find the angles of the triangle.
Solution:
Given, ABC is a triangle.
Also, ∠A = ∠C
Exterior angle, ABX = 140°
We have to find the angles of the triangle.
Exterior angles are defined as the angles formed between the side of the polygon and the extended adjacent side of the polygon.
From the figure,
The exterior angle is ∠ABX = 140°.
The exterior angle theorem states that the measure of an exterior angle is equal to the sum of the measures of the two opposite interior angles of the triangle.
By exterior angle property,
∠ABX = ∠A + ∠C
∠ABX = ∠A + ∠A
140° = 2∠A
∠A = 140°/2
∠A = 70°
So, ∠A = ∠C = 70°
Angle sum property of a triangle states that the sum of all three interior angles of a triangle is always equal to 180 degrees.
By angle sum property,
∠A + ∠B + ∠C = 180°
70° + ∠B + 70° = 180°
140° + ∠B = 180°
∠B = 180° - 140°
∠B = 40°
Therefore, the angles are 70°, 40° and 70°.
✦ Try This: Find the value of the exterior angle.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 124
In ∆ABC, if ∠A = ∠C, and exterior angle ABX = 140°, then find the angles of the triangle.
Summary:
In ∆ABC, if ∠A = ∠C, and exterior angle ABX = 140°, then the angles of the triangle are 70°, 40° and 70°.
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