EXTERIOR AND INTERIOR ANGLES OF TRIANGLE.

 WELCOME.

ENJOY MATH WITH AMJID.

jkeduhubthroughanimation.com

EXTERIOR AND INTERIOR ANGLES OF TRIANGLE.

Suppose one side of a triangle ABC, say BC, is produced to D, then

is called the Exterior angle. With respect to the exterior

is called the adjacent angle while

and

are called Interior opposite angles.

Relation between exterior angle and the pair of interior opposite angles.
If the side of a triangle is produced the exterior angle so formed is equal to the sum of interior opposite angles.

First Method
Proof :

In other words, exterior angle is greater than either of the interior opposite angles.

Second Method

Illustrative Examples
Example 1. An exterior angle of a triangle is of measure 70° and one of its interior opposite angles is of measure 25°. Find the measure of the other interior opposite angle.
Solution.

Example 2. The two interior opposite angles of a triangle are 60° and 80°. Find the measure of the exterior angle.
Solution.

Example 3. In the given figure, find the value of x and y.

Solution. In the given figure, side BC of

is produced to D, forming exterior

But we know that an exterior angle of a triangle is equal to the sum of its interior opposite angles.

Example 4. Find the value of the unknown exterior angle x in the following diagrams :

Solution. We know that, in a triangle, an exterior angle is equal to the sum of the two interior opposite angles, therefore,
(i) x = 50° + 70° = 120°
(ii) x = 65° + 45° = 110°
(iii) x = 60° + 60° = 120°

Example 5. Find the value of unknown interior angle x in the following diagrams :

Solution. We know that, in a triangle, an exterior angle is equal to the sum of the two interior opposite angles, therefore,

OK THANKS.

PLEASE LIKE SHARE AND FOLLOW.