In the adjacent figure ray OS stands on a line PQ. Ray OR and ray OT are angle bisectors of `anglePOS` and `angleSOQ` respectively. Find `angleROT`.

In Fig., ray OS stand on a line POQ Ray OR and ray OT are angle bisectors of ∠POS and ∠SOQ respectively. If ∠POS=x, find ∠ROT.

In the adjacent figure lines PQ and RS intersect each other at point O. If anglePOR : angleROQ = 5: 7, find all the angles.

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

In the adjacent figure m || n. A, B are any two points on m and n respectively. Let ‘C’ be an interior, point between the lines m and n. Find angleACB .

In the adjoining figure, ray PQ touches the circle at point Q. Line PRS is a secant, If P=12, PR=8 then PS and RS

In the adjacent figure, AB || CD, ‘t’ is a transversal intersecting E and F respectively. If ∠2 : ∠1 = 5 : 4, find the measure of each marked angles.

In the adjacent figure PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflected back along CD . Prove that AB || CD.

It is given that angleXYZ= 64^(@) and XY is produced to point P. A ray YQ bisects angleZYP . Draw a figure from the given information. Find angleXYQ and reflex angleQYP .

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