In the given figure lines `bar(XY)` and `bar(MN)` intersect at O. If `∠POY = 90^(@)` and a: b = 2 : 3, find c.

In the given figure lines bar(AB) and bar(CD ) intersect at O. If angleAOC+ angleBOE= 70^(@) and angleBOD = 40^(@) , find angleBOE and reflex angleCOE .

In the given figure three lines bar(AB) , bar(CD) and bar(EF) intersecting at O. Find the values of x, y and z it is being given that x : y : z = 2 : 3 : 5

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 given figure if line segments PQ and RS intersect at point T, such that anglePRT = 40^(@), angleRPT = 95^(@) and angleTSQ = 75^(@) , find angleSQT

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 given figure AS || BT, angle4 = angle5 bar(SB) bisects angleAST . Find the measure of angle1

In the given figure A,B,C and D are four points on a circle, AC and BD intersect at a point E such that angleBEC=130^(@) and angleECD=20^(@) . Find angleBAC .

Any circle through the point of intersection of the lines x+sqrt(3)y=1 and sqrt(3)x-y=2 intersects these lines at points Pa n dQ . Then the angle subtended by the arc P Q at its center is (a) 180^0 (b) 90^0 (c) 120^0 depends on center and radius

Write in the rectangular form bar(3i) + (1)/(2 - i)