# 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.*