Question

Which of the following is true?
A.m< LSO+m<MSO=180 
B. <LSM\cong<NSM
C. m <LSM+m <SML+ m<MLS+360
D.m<NSO+m< OSL+m<LSM+ m <MSN=360
D is correct but i don't know why how do i do this problem

Answer 1

A. It is wrong because MSO is 180° itself
B. It is wrong because if it was true then according to linear pair property.. both of the angles would be right angles.But it isn't ...so there
C.It is wrong as angle sum property states that sum of all the angles of a triangle is equal to 180°
D.It is correct as let NSO be X and let LSO be y...

according to opposite angles property ( or whatever it is called) NSO=LMS
and LSO=MSN
Now
according to linear pair
NSO+LSO=180°
MSN+LMS=180°
I.E.
X+Y=180° and X+Y=180°
SO 2X+2Y=180+180=360°
i.e. sum of all those angles is 360°

BAM..Hope this helps