Selina Concise Class 6 Math Chapter 25 Quadrilateral Exercise 25B Solution
EXERCISE 25B
(1) ∠A + ∠B = 180o
⇒ 78o + ∠B = 180o
⇒ ∠B = 180o – 78o = 102o
∠C + ∠D = 180o
⇒ 120o + ∠D = 180o
⇒ ∠D = 180o – 120o = 60o
(2) ∵ AB ∥ DC and BC is transversal
∴ ∠A and ∠B are co-interior angles with their sum = 180o
Then, ∠A + ∠D = 180o
⇒ x + (3x – 20) = 180o
⇒ x + 3x – 20 = 180o
⇒ 4x = (180 + 20)o = 200o
⇒ x = 50o
(3) As the trapezium ABCD is a quadrilateral,
∴ Sum of interior angles = 360o
⇒ ∠A + ∠B + ∠C + ∠D = 360o
⇒ 3x + 4x + 5x + 6x = 360o
⇒ 18x = 360o
⇒ x = 20o
∠A = 3x = 3 × 20 = 60o
∠B = 4x = 4 × 20 = 80o
∠C = 5 × 20 = 100o
∠D = 6 × 20 = 120o
AB is parallel to DC
∵ ∠A + ∠D = 180o
(4) In an isosceles trapezium one pair of opposite sides are parallel to each other and the other pair of opposite sides are equal to each other.
(5) ∵ The diagonals of an isosceles trapezium are of equal length.
∴ 3x – 8 = x
⇒ 3x – x = 8
⇒ 2x = 8
⇒ x = 4
The value of x = 4.
(6) Since, the base angles of an isosceles trapezium are equal.
∴ ∠A + ∠D = 180o
⇒ 115o + ∠D = 180o
⇒ ∠D = 180o – 115o = 65o
Also, ∠D = ∠C = 115o
(7) ∠A + ∠B = 180o
⇒ 100o + ∠B = 180o
⇒ ∠B = 180o – 100o = 80o
Also opposite angles, ∠B = ∠C = 80o
And, ∠A = ∠D = 100o
(8) We know, the opposite angles of a parallelogram are equal.
∴ ∠A = ∠C = 70o and ∠D = ∠B = 110o.
(9) We know that sum of interior angles of a quadrilateral is 360o.
⇒ ∠A + ∠B + ∠C + ∠D = 360o
⇒ 2x + 3x + 2x + 3x = 360o
⇒ 10x = 360o
⇒ x = 36
∴ ∠A = ∠C = 2 × 36 = 72o
And ∠B = ∠D = 3 × 36 = 108o
(10) (i) ∠A + ∠B = 180o
⇒ 90o + ∠B = 180o
⇒ ∠B = 180o – 90o = 90o
(ii) The name of the given parallelogram is rectangle.
(13) We know, in a rectangle diagonals are equal.
∴ AC = BD = 18 cm
(14) We know, sum of all angles of a quadrilateral is 360o.
(i) ∴ 4 (x + 5) = 360
⇒ 4x + 20 = 360
⇒ 4x = 360 – 20 = 340
⇒ x = 85
(ii) Each of the angle = (x + 5)o = (85 + 5)o = 90o
Name of the quadrilateral is rectangle.
(15) Let the fourth angle be xo.
∴ x + (3 × 90) = 360
⇒ x + 270 = 360
⇒ x = 360 – 270 = 90o
Therefore, the given quadrilateral is a rectangle.
(16) The diagonals of a rhombus always intersect 90o.
(17) Since, AB = BC = CD = DA = 6 cm
∴ The given figure is a rhombus.
This figure will be a square if any angle is 90o.
(18) (i) The all side must be equal.
(ii) Any angle is 90o.