Lines and Angles

Exercise 1

1.    Find the complement of each of the following angles:

2.    Find the supplement of each of the following angles:

3.   Identify which of the following pairs of angles are complementary and which are supplementary:

(i) 65°, 115°                      (ii) 63°, 27°                      (iii) 112°, 68°

(iv) 130°, 50°                    (v) 45°, 45°                      (vi) 80°, 10°

4.    Find the angle which is equal to its complement:

5.    Find the angle which is equal to its supplement.

6.    In the given figure, ∠ 1 and ∠ 2 are supplementary angles. If ∠ 1 is decreased, what changes should take place in ∠ 2 so that both the angles still remain supplementary?

7.    Can two angles be supplementary if both of them are:

(i) acute                 (ii) obtuse              (iii) right?

8.   An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°?

9.    In the adjoining figure:

(i) Is ∠ 1 adjacent to ∠ 2?

(ii) Is ∠ AOC adjacent to ∠ A0E?

(iii) Do ∠ COE and ∠ EOD form a linear pair?

(iv) Are ∠ BOD and ∠ DOA supplementary?

(v) Is ∠ 1 vertically opposite to ∠ 4?

(vi) What is the vertically opposite angle of ∠ 5?

10.  Indicate which pairs of angles are:

Vertically opposite angles?

Linear pairs?

11.  In the following figure, is ∠ adjacent to ∠ 2? Give reasons.

12.  Find the values of the angles x, y and z in each of the following:

13.  Fill in the blanks:

(i) If two angles are complementary, then the sum of their measure is _____.

(ii) If two angles are supplementary, then the sum of their measure is ___.

(iii) Two angles forming a linear pair are _____.

(iv) If two adjacent angles are supplementary, they form a ____.

(v) If two lines intersect a point, then the vertically opposite angles are always ___.

(vi) It two lines intersect at a point and if one pair of vertically opposite angles are acute angles, them the other pair of vertically opposite angles are ____.

14.  In the adjoining figure, name the following pairs of angles:

(i) Obtuse vertically opposite angles.

(ii) Adjacent complementary angles.

(iii) Equal supplementary angles.

(iv) Unequal supplementary angles.

(v) Adjacent angles that do not form a linear pair.

Exercise 2

15.  State the property that is used in each of the following statements:

(i) If a || b, then ∠ 1 = ∠ 5.

(ii) If ∠ 4 = ∠ 6, then a

(iii) If ∠ 4 + ∠ 5 + 180°, then a || b.

16.  In the adjoining figure, identify:

(i) the pairs of corresponding angles.

(ii) the pairs of alternate interior angles.

(iii) the pairs of interior angles on the same side of the

(iv) the vertically opposite angles.

17.  In the adjoining figure, p || q. Find the unknown angles.

18.  Find the values of x in each of the following figures if l || m.

19.  In the given figure, the arms of two angles are parallel. If ΔABC = 70°, then find:

(i) ∠ DGC             (ii) ∠ DEF

20.  In the given figures below, decide whether l is parallel to m.