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

Explanation:

Consider an ∆XYZ, as shown in the figure below.

Construction: draw a line ST parallel to the side YZ of the triangle.

Since ST is a straight line, we can say that

∠SXY + ∠YXZ + ∠ZXT = 180° ……… (1)

Since ST||YZ and XY, XZ are transversals,

Therefore,

∠ZXT = ∠XZY (a pair of alternate angles)

∠SXY = ∠ZYX (a pair of alternate angles)

On substituting the value of ∠ZXT and ∠SXY in equation (1),

∠XZY + ∠YXZ + ∠ZYX= 180°

Finale Answer:

THUS, The sum of the interior angles of a triangle is 180°.