Lines and Angles-Test

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.

5.  

      

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.