Question

Prove that the sum of angles of a triangle is 180 °.​

Answer 1

Answer:Hii dear here is your answer

In order to prove that the sum of angles of a triangle is 180, you must know the theorems of angles of a triangle.We know that,  alternate interior angles are of equal magnitude.This'll help us get the answer. Let us assume a triangle ABC. Now we have to substitute the angles.∠PAB + ∠BAC + ∠CAQ = 180°. where PQ line parallel to side BC touching vertex A.∠PAB = ∠ABC & ∠CAQ = ∠ACB BECAUSE alternate interior angles are congruent..Hence we get, ∠ABC + ∠BAC + ∠ACB = 180°   [Proved]

Hope it's help u

Answer 2

Question:Prove that the sum of angles of a triangle is 180°

Given:

A ∆ABC

To prove:

<1+<2+<3=180°

Construction:

Through A, draw a line DAE||BC

Proof:

DAE||BC and AB is transversal

<4=<2 (Alternate int angle)

DAE||BC and AC is transversal

<5=<3 (Alternate int angle)

Now

DAE is a straight line

<4+<1+<5=180° (angle on the same side of DAE at the point A)

<1+<4+<5=180°

<1+<2+<3=180°. {<4=<2 and <5=<3}

Hence;The sum of the angles of a triangle is 180°