lines and angles

1. Q1. Define and the following terms: (i) Angle (ii) Obtuse angle (iii) Complementary angles (iv) Supplementary angles (v) Adjacent angles 
2. Define and draw the following: (i) Linear pair of angles (ii) Vertically opposite angles
3. Find the complement of the following angles: (i) 58 (ii) 45 
4. Find the supplement of the following angles: (i) 90 (ii) 120  
5. Two supplementary angles are in the ratio 3:2. Find the angles. 
6. One of the four angles formed by two intersecting lines is a right angle. Show that the other three angles will also be right angles
7. Fill in the blanks to make the following statements true:
   (i) If two parallel lines are intersected by a transversal, then each pair of corresponding angles are ... .
   (ii) Two lines parallel to the same line are
   ... each other.
   (iii) If a transversal intersects two lines in such a way that the sum of interior angles on the same side of the transversal is 180∘then the lines are ... . 
8. Prove that the two lines which are both parallel to the same line are parallel to one another
9. Two parallel lines are cut by a transversal such that one of the interior angles is 57. Find each of the interior angles. 
10. If ray OS stands on a line POQ. Rays OR and OT are the angle bisectors of < POS and < SOQ respectively.  If < POS = x. Find < ROT