Lines and Angles-Sample Papers

1.  In the figure, lines PQ and RS intersect each other at a point O. If ∠POR : ∠ROQ = 5 : 7, find all the angles.

      

2.  In the figure, OS stands on a line POQ. Ray OR and ray OT are angle bisectors of ∠POS and ∠SOQ, respectively, if ∠POS = x, find ∠ROT.

      

3.  In the figure, OP, OQ, OR and OS are four rays. Prove that : ∠POQ + ∠QOR + ∠SOR + ∠POS = 360°.

      

4.  Two adjacent angles on a straight line are in the ratio 2:3. Find the measures of each one of these angles.

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6.  If two lines intersect each other, then show that the vertically opposite angles are equal.

7.  For what value of x will the lines l and m be parallel to each other?

      

8.  If parallel lines are intersected by the transversal, prove that the bisectors of the two pairs interior angles enclose a rectangle.

9.  If the arms of an angle are respectively parallel to the arms of another angle, prove that the two angles are equal or complementary.

10.  In a triangle ABC, if the sum of angle A and B is 150� and angle B and C is 100�. What is the measure of each angle.