Maharashtra State BoardSSC (English Medium) 7th Standard
Advertisement Remove all ads

Exterior Angle of a Triangle and Its Property

Advertisement Remove all ads

Topics

description

  • An exterior angle of a triangle is equal to the sum of its interior opposite angles.
  • The sum of exterior angles of a triangle is 360°.

definition

  • Exterior angle: On extending one side of a triangle, the angle obtained which forms a linear pair with the adjacent interior angle of the triangle is called an exterior angle of that triangle.

notes

Exterior angle of a triangle Property:

  • An exterior angle of a triangle is formed when a side of a triangle is produced.

  • At each vertex, you have two ways of forming an exterior angle.

               

  • Observe the angle ACD formed at point C. This angle lies in the exterior of ∆ABC. We call it an exterior angle of the ∆ABC formed at vertex C.
  • Clearly ∠BCA is an adjacent angle to ∠ACD. The remaining two angles of the triangle namely ∠A and ∠B are called the two interior opposite angles or the two remote interior angles of ∠ACD.
  • m∠ACD = m ∠A + m ∠B
  • In the figure alongside, all exterior angles of a triangle are shown. a, b, c, d, e, f are the exterior angles of ∆PQR. In the same way, every triangle has six exterior angles.

         

theorem

A property of exterior angles:

The measure of any exterior angle of a triangle is equal to the sum of the measures of its interior opposite angles.

Given: Consider △ ABC. ∠ ACD is an exterior angle.

To Show: m∠ ACD = m∠ A + m∠ B. Through C draw `bar"CE"`, parallel to `bar"BA"`.

Justification:

Steps Reasons
(a) ∠1 = ∠x

`bar"BA" || bar"CE" and bar"AC"` is a transversal.
Therefore, alternate angles should be equal.

(b) ∠2 = ∠y

`bar"BA" || bar"CE" and bar"BD"` is a transversal.
Therefore, the corresponding angles should be equal.

(c) ∠ 1 + ∠ 2 = ∠ x + ∠ y  
(d) Now, ∠ x + ∠ y = m∠ ACD From given Figure
Hence, ∠ 1 + ∠ 2 = ∠ ACD  

Thus, The measure of any exterior angle of a triangle is equal to the sum of the measures of its interior opposite angles.

Example

Find angle x in Fig

Sum of interior opposite angles = Exterior angle
or     50° + x = 110°
or     x = 60°

If you would like to contribute notes or other learning material, please submit them using the button below.

Shaalaa.com | Exterior angle of a triangle Property

Shaalaa.com


Next video


Shaalaa.com


Exterior angle of a triangle Property [00:05:29]
S
Series: Exterior Angle of a Triangle
0%


Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×