construction: draw ray OA opposite to Ray OQ.such that A - O - Q.
proof:-
ray OA and ray OQ are opposite rays. ( by construction ) so, angle POA and angle POQ form a linear pair. (by linear pair axiom) therefore angle POA + angle POQ = 180 (equation 1 ) ray OA and ray OQ are opposite rays. ( by construction ) so, angle AOR and angle ROQ form a linear pair. (by linear pair axiom) therefore Angle AOR + Angle ROQ = 180 (equation 2) adding equation 1 and 2 we get, angle POA + angle POQ + Angle AOR + Angle ROQ = 180 + 180
Answers & Comments
construction: draw ray OA opposite to Ray OQ.such that A - O - Q.
proof:-
ray OA and ray OQ are opposite rays.
( by construction )
so, angle POA and angle POQ form a linear pair. (by linear pair axiom)
therefore angle POA + angle POQ = 180
(equation 1 )
ray OA and ray OQ are opposite rays.
( by construction )
so, angle AOR and angle ROQ form a linear pair. (by linear pair axiom)
therefore Angle AOR + Angle ROQ = 180
(equation 2)
adding equation 1 and 2 we get,
angle POA + angle POQ + Angle AOR + Angle ROQ = 180 + 180
angle POA + angle POQ + (angle AOS + Angle SOR) + Angle QOR = 360
(by angle addition property)
angle POA + angle AOS + angle POQ + angle SOR + angle QOR = 360
(by angle addition property) therefore ,
angle POQ + angle QOR + angle SOR + angle QOR = 360
(by angle addition property)
hence, proved.