Question

how can we prove that sum of all angles of triangles is 180???

Answer 1

I can prove it
we know that the sum of all angles =180°
so, x+x+x=180°
3x=180°
and then x=3/180°
60°+60°+60°=180°
180°=180°
I hope it's help you
thanks

Answer 2

❤❤Here is your answer ✌ ✌

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Draw a line parallel to side BC of the triangle that passes through the vertex A.




the equation angle PAB + angle BAC + angle CAQ = 180 degrees.--------------(1)


State that angle PAB = angle ABC and angle CAQ = angle ACB. ------------(2)

Equation 2: angle PAB = angle ABC
Equation 3: angle CAQ = angle ACB

It is a geometric theorem that alternate interior angles of parallel lines are congruent.

Substitute angle PAB and angle CAQ in Equation 1 for angle ABC and angle ACB (as found in Equation 2 and Equation 3) respectively. 

Thus we get, Angle ABC + angle BAC + angle ACB = 180°.In other words, in the triangle ABC, angle B + angle A + angle C = 180°. Thus, the sum of all the angles of a triangle is 180°.