Question

Prove that - the measure of an exterior angle of a triangle is equal to the sum of its remote interior angle​

Answer 1

Answer:

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. (Non-adjacent interior angles may also be referred to as remote interior angles.) FACTS: An exterior ∠ is equal to the addition of the two Δ angles not right next to it.

Answer 2

Answer

Supposed a triangle ABC of side AB, BC And CA and Angle are <1, <2 and <3

Now extended a side AB of the length it became a exterior angle.

We have to prove that

$<1+<3=<4$

We know that sum of all angles of triangle is 180 degree

$< 1 + < 2 + < 3 = 180 {}^{0} \\ (1.)$

And sum of angle in a straight line is 180 degree

$< 2 + < 4 = 180 {}^{0} \\ (2.)$

Now from equation (1) and (2) we will get the equation

$< 1 + < 2 + < 3 = < 2 + < 4 \\ < 1 + < 3 = < 4$

Hence Proved