Question

Prove that an exterior angle of a triangle is equal to the sum of its interior opposite angles .​

Answer 1

hello!!

as we know by angle sum property of triangle the all angles of a triangle add up to 180°.

let's take an example of an exterior angles being

so if we take as an linear pair the adjacent angle would be 60°

now by asp of a triangle. the sum of other two angles 180-60=120

which the the exterior angle

hence by above example we can prove the status

Answer 2

Answer:

let's take a example :

exterior angle =135°

angle sum property of triangle =180°

adjacent angle of exterior angle =180-135=45°

now subtract 45 from 180 ( 45 is adjacent angle of exterior angle and 180 is sum of all angles of triangle )

you will find the sum of two angles opposite to adjacent angle

180-45=135°

.•. exterior angle and and two opposite angles of adjacent angle is equal

hence proved