what is exterior angle property?

Dear Student!

The angle formed by a side with its extended adjacent side of a triangle is called an exterior angle of the triangle.
Exterior angle property states that the measure of exterior angles of a triangle is equal to the sum of its two interior opposite angles.
Example:
Find the value of x in the given figure.
Solution:
Exterior angle = Sum of opposite interior angles
x = 60° + 60°
x = 120°

Cheers!

  • 15

An Exterior Angle

An angle which is present outside a shape is known as exterior angle.

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An exterior angle of a triangle is equal to the sum of its interior opposite angles.

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The exterior angle theorem is a theorem in elementary geometry which states that the exterior angle of a triangle is equal to the sum of the two remote interior angles.

A triangle has three corners, called vertices. The sides of a triangle that come together at a vertex form an angle. This angle is called the interior angle. In the picture below, the angles a, b and c are the three interior angles of the triangle. An exterior angle is formed by extending one of the sides of the triangle; the angle between the extended side and the other side is the exterior angle. In the picture, angle d is an exterior angle.

The exterior angle theorem says that the size of an exterior angle at a vertex of a triangle equals the sum of the sizes of the interior angles at the other two vertices of the triangle. So, in the picture, the size of angle d equals the size of angle a plus the size of angle c.

Remint3.svg

 

Given: In ∆ABC, angle ACD is the exterior angle.

To prove: Angl-sym.gifACD = Angl-sym.gifABC + Angl-sym.gifBAC (here, Angl-sym.gifACD denotes the size of the angle ACD)

Proof:

StatementsReason
In ∆ABC, Angl-sym.gifa + Angl-sym.gifb + Angl-sym.gifc = 180°------[1]Sum of the measures of all the angles of a triangle is 180°
Also, Angl-sym.gifb + Angl-sym.gifd = 180°-------[2]Linear pair axiom
Angl-sym.gifa + Angl-sym.gifc + Angl-sym.gifb = Angl-sym.gifb + Angl-sym.gifdFrom [1] and [2]
Angl-sym.gifa + Angl-sym.gifc + Angl-sym.gifb = Angl-sym.gifb +mAngl-sym.gifd 
Angl-sym.gifd = Angl-sym.gifa + Angl-sym.gifc
i.e. Angl-sym.gifACD = Angl-sym.gifABC + Angl-sym.gifBAC 

Hence, proved.

Best Wishes !@

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exterior angle is th esum of the opposite angles

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this is the right answer

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yes offf course it is right

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 great job!

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