Section outline

    • Solutions to Ex. 5.1
      Q1. Find the complement of each of the following angles:

      Ans:

      (i) The complement of 20º = 90º - 20º = 70º

      (ii) The complement of 63º = 90º – 63º = 27º

      (iii) The complement of 57º = 90º – 57º = 33º

      Q2. Find the supplement of each of the following angles:

      Ans:

      (i) The supplement of 105º = 180º - 105º = 75º

      (ii) The supplement of 87º = 180º – 87º = 93º

      (iii) The supplement of 154º = 180º – 154º = 26º

      Q3. Identify which of the following pairs of angles are complementary and which are supplementary.

      Ans:

      (i) 65º, 115º

      Adding both the angles,

      65º + 115º = 180º

      Thus, the angles are supplementary.

      (ii) 63º, 27º

      Adding both the angles,

      63º + 27º = 90º

      Thus, the angles are complementary.

      (iii) 112º, 68º

      Adding both the angles,

      112º + 68º= 180º

      Thus, the angles are supplementary.

      (iv) 130º, 50º

      Adding both the angles,

      130º + 50º = 180º

      Thus, the angles are supplementary.

      (v) 45º, 45º

      Adding both the angles,

      45º + 45º = 90º

      Thus, the angles are complementary.

      (vi) 80º, 10º

      Adding both the angles,

      80º + 10º = 90º

      Thus, the angles are complementary.

      Q4. Find the angle which is equal to its complement.

      Ans:

      Let the angle be x.

      The complement = x (as, angle = complement)

      The sum of measure complementary angle pair is 90º.

      x = x = 90

      2x = 90

      x = 45

      The angle is 45º.

      Q5. Find the angle which is equal to its supplement.

      Ans:

      Let the angle be x.

      The supplement = x (as, angle = supplement)

      The sum of measure supplementary angle pair is 180º.

      x = x = 180

      2x = 180

      x = 90 

      The angle is 90º.

      Q6. 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.

      Ans:

      Given: ∠1 + ∠2 = 180° 
      If ∠1 is decreased, then measure of∠2 must be increased by the same degree so that both the angles still remain supplementary.

      Q7. Can two angles be supplementary if both of them are: (i) acute? (ii) obtuse? (iii) right?

      Ans:

      (i) If two angles are acute, i.e. each measures less than 90º.

          Then their sum will be less than 180º. So, two acute angles cannot be supplementary.

      (ii) If two angles are obtuse, i.e. each measures more than 90º.

           Then their sum will be more than 180º. So, two obtuse angles cannot be supplementary.

      (iii) If two angles are rìght i.e. each measures 90º.

           Then their sum will be = 90º + 90º = 180º. So, two right angles are supplementary.

      Q8. An angle is greater than 45º. Is its complementary angle greater than 45º or equal to 45º or less than 45º?

      Ans:

      Let the given angle be xº.

      Complementary angle = (90 - x)º

      x > 45

      adding complementary angle to both sides,

      x + 90 - x > 45 + 90 - x

      Thus, 45 > x

      The complementary angle will be less than 45º.

      Q9. Fill in the blanks:

      Ans:

      (i) 90º

      (ii) 180º

      (iii) Linear pair

      Q10. In the adjoining figure, name the following pairs of angles.

      Ans:

      (i) ∠BOC and ∠AOD are obtuse vertically opposite angles.

      (ii) ∠AOB and ∠EOA are adjacent complementary angles.

      (iii) ∠EOD and ∠EOB are equal supplementary angles.

      (iv) ∠AOB and ∠AOD are unequal supplementary angles

      (v) ∠EOD and ∠DOC are adjacent angles that do not form a linear pair.

       

    • Solutions to Ex. 5.2
      Q1. State the property that is used in each of the following statements?

      Ans:

      (i) Corresponding angle property.

      (ii) Alternate interior angle property.

      (iii) Interior angles on the same side of the transversal are supplementary.

      Q2. In the adjoining figure, identify the following:

      Ans:

      (i) ∠1 & ∠5, ∠2 & ∠6, ∠4 & ∠8, ∠3 & ∠7.

      (ii) ∠2 & ∠8, ∠3 & ∠5.

      (iii) ∠2 & ∠5, ∠3 & ∠8.

      (iv) ∠1 & ∠3, ∠2 & ∠4, ∠5 & ∠7,  ∠6 & ∠8.

      Q3. In the adjoining figure, p || q. Find the unknown angles.

      Ans:

      ∠e + 125 = 180 (Linear pair)

      ∠e = 55°

      ∠f = 55° (Vertically opposite angles)

      By corresponding angle property,

      ∠d = 125°

      ∠e = ∠a = 55° &

      ∠f = ∠c = 55°

      ∠b = 125° (vertically opposite angle to ∠d)

      Q4. Find the value of x in each of the following figures if l || m.

      Ans:

      (i) Let the angle adjacent to 110º be y.

      110 + y = 180 (Linear pair)

      y = 70º

      As l || m, x = y (corresponding angle property)

      ∠x = 70º

      (ii) As l || m, by corresponding angle property

      ∠x = 100º 

      Q5. In the given figure, the arms of two angles are parallel. If ∠ABC = 70º, then find:

      Ans:

      Given : ∠ABC = 70º

      (i) As AB || DG & BC is the transversal,

      ∠DGC = 70º (corresponding angle property)

      (ii) As BC || EF & DE is the transversal,

      ∠DEF = 70º (corresponding angle property)

      Q6. In the given figures below, decide whether l is parallel to m.

      Ans:

      (i) Using sum of interior angle on the same side of the transversal are supplementary,

      126° + 44° = 170°

      As 170° \( \neq \) 180°

      Line l is not parallel to line m.

      (ii) Let the vertically opposite angle to ∠75° be x.

      x = 75°

      Using sum of interior angle on the same side of the transversal are supplementary,

      x + 75 = 75 + 75 = 150°

      As 150° \( \neq \) 180°

      Line l is not parallel to line m.

      (iii) Let the vertically opposite angle to ∠57° be x.

      x = 57°

      Using sum of interior angle on the same side of the transversal are supplementary,

      x + 123 = 57 + 123 = 180°

      Line l is parallel to line m.

      (iv) Let the vertically opposite angle to ∠72° be x.

      x = 72°

      Using sum of interior angle on the same side of the transversal are supplementary,

      x + 98 = 72 + 98 = 170°

      As 170° \( \neq \) 180°

      Line l is not parallel to line m.