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 the adjoining figure, BX and CY are the bisectors of angle ABC and angle ACB respectively. If AB=AC and BY=4 cm, then find the lengths of AX.

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 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

In the adjacent figure, ABC is a triangle in which angleB = 50^(@) and angleC = 70^(@) . Sides AB and AC are produced. If ‘z’ is the measure of the angle between the bisectors of the exterior angles so formed, then find 'z'.