<1 + <2 + <3 = 180°
CONSTRUCTION.
Draw a line xy passes through p parallel to QR
PROOF.
For line XY AND QR
with TRANSVERSAL QR
<2 = <4 = ....(1) [ Alternate angles ]
<3 = <5 = .....(2) [ Alternate angles ]
Also for a line XY
<1 + <4 + <5 = 180° [Linear pair ]
From equation (1) and (2) we get,
<1 + <2 + <3 = 180°
HENCE,
The sum of all angles of triangle is = 180°
HENCE PROVED.
Note for diagram see the image attachment.
