Question

can you solve this problem.....

Answer 1

please mark as brainliest.

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.