Exterior Angle Property


Triangles and its Properties II - Concepts
Class - 7th CBSE Subjects
 
 
Concept Explanation
 

Exterior Angle Property

Exterior Angle Property:

An exterior angle of a triangle is equal to the sum of the opposite interior angles. If the equivalent angle is taken at each vertex, the exterior angles always add to 360° In fact, this is true for any convex polygon, not just triangles.

Exterior Angle Property of a Triangle states that measure of exterior angle of a triangle is equals to the sum of measures of its interior opposite angles.In order words:Exterior Angle = Sum of Interior Opposite Angles As shown in the following diagram:Exterior Angle is ∠ ACD and its two interior opposite angles are ∠ BAC and ∠ ABCMeasure of ∠ ACD = 130°Measure of one interior ∠ BAC = 60°Measure of other interior ∠ ABC = 70°Now, we can observe that:130° = 60° + 70°Or we can say:∠ ACD = ∠ BAC and ∠ ABCHence, its demonstrated that measure of exterior angle of a triangle is equals to the sum of measures of its interior opposite angles  

Sample Questions
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Question : 1

find the measure of angle angle QRX in the following triangle

Right Option : A
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Question : 2

An exterior angle of a triangle is 105^0 and its two interior opposite angles are equal. Each of these equal angles is ___________________.

Right Option : B
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Question : 3

An exterior angle of a triangle is 108^0 and its interior opposite angles are in the ratio 4:5.The angles of the triangle are

Right Option : A
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