In the given figure, ray OS stands on a lien POQ. Ray OR and ray OT are angle bisectors of `anglePOS` and `angleSOQ` respectively. If `anglePOS=x`, find `angleROT`.

In the given figure angleA= 40^(@) . If bar(BO) and bar(CO) are the bisectors of angleB and angleC respectively. Find the measure of angleBOC .

In the given figure, angleX=62^(@),angleXYZ=54^(@) . If YO and ZO are the bisectors of angleXYZ and angleXZY respectively of DeltaXYZ , find angleOZY and angleYOZ .

Ray AX is the bisector of angleBAC and ray AY is the bisector of angleXAC . If angleBAY=60^(@) , find angleBAC .

In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that.

In the above figure (ray diagram), state the angle of incidence and the angle of deviation.

In the given figure, OP, OQ, OR and OS are four rays. Prove that anglePOQ+angleQOR+angleSOR+anglePOS=360^(@) .

In the figure above (no to scale), l ||m and also x:y = 5:3 . Find the measure of angles (x-40^(@)) and (y+40^(@)) respectively.

Ray EX is the bisector of angleDEF and ray EY is the bisector of angleDEX . If angleDEX=42^(@) , find angleYEF and angleDEF .

In the above figure (ray diagram), state angle of incidence, angle of emergence and angle of deviation.

In the given figure bar(PQ) is a line. Ray bar(OR) is perpendicular to line bar(PQ) . bar(OS) is another ray lying between rays bar(OP) and bar(OR) . Prove that angleROS = (1)/(2) angleQOS − anglePOS