Question

show the sum of all angles in a triangles is 180 digree

Answer 1

RTP:-sum of all angles in a triangles is 180 digree

Const :-We draw a line parallel to AB that passes

through point C.  {see the diagram}

Angles C and C' are vertical angles,

∴ ∠C = ∠C'.

Angles B and B' are corresponding angles,

therefore ∠B = ∠B'.

∠ A and ∠ A' are corresponding angles, therefore ∠A = ∠A'.

So, the angle sum ∠A + ∠B + ∠C is equal to the angle sum ∠A' + ∠B' + ∠C'.

The three angles A', B', and C' form together a straight angle (they are along the line l).

So, their angle sum is 180°. But then the angle sum ∠A + ∠B + ∠C must also be 180°.

Answer 2

To prove this we are given a triangle PQR and Angle 1, Angle 2 and Angle 3 are the angles of triangle PQR.

To prove Angle 1 + A angle 2 + Angle 3 = 180 degree, draw a line XYP parallel to QR through the opposite vertex P.

XPY is a line,

Therefore, Angle 4 + Angle 1 + angle 5 = 180 degree                              (1)

XPY || QR and PQ,PR are transvesals  

Angle 4 = Angle 2   &

Angle 5 = Angle 3 ( Pairs of alternate angles)

Substituting Anggle 4 and Angle 5 in (1) we get

Angle 2 + Angle 1 + Angle 3 = 180 dgree  

i.e. Angle 1 + Angle 2 + Angle 3 = 180 degree