Selina Concise Class 6 Math Chapter 24 Triangles Exercise 24A Solution
EXERCISE 24A
(1) In each of the following, find the marked unknown angles:
(i) We know, measure of 3 angles of a triangle is 180o.
Then, 70 + 72 + z = 180
⇒ x + 142 = 180
⇒ x = 180 – 142
⇒ x = 38o
(ii) a + 40 + 45 = 180
⇒ a + 85 = 180
⇒ a = 180 – 85
⇒ a = 95o
And, b + 50 + 80 = 180
⇒ b + 130 = 180
⇒ b = 180 – 130
⇒ b = 50o
(2) Can a triangle together have the following angles?
(i) 55 + 55 + 80 ≠ 180
(ii) 33 + 74 + 73 = 180
(iii) 85 + 95 + 22 ≠ 180
(3) Find x, if the angles of a triangles are:
(i) x + x + x = 180
⇒ 3x = 180
⇒ x = 60
(ii) x + 2x + 2x = 180
⇒ 5x = 180
⇒ x = 36
(iii) 2x + 4x + 6x = 180
⇒ 12x = 180
⇒ x = 15
(4) We know, one angle of right triangle is 90o.
Let the required angle be x.
∴ x + 90 + 60 = 180
⇒ x + 150 = 180
⇒ x = 180 – 150 = 30o
Therefore, the acute angle is 30o.
(5) Let the ∠C = xo.
We know, ∠A + ∠B + ∠C = 180
⇒ 62 + 62 + x = 180
⇒ x + 124 = 180
⇒ x = 180 – 124 = 56o
(6) Let the ∠B and ∠C = xo
We know, ∠A + ∠B + ∠C = 180
⇒ x + x + 100 = 180
⇒ 2x = 180 – 100
⇒ 2x = 80
⇒ x = 40
Therefore, ∠B = 40o
(7) Find, giving reasons, the unknown marked angles in each triangle drawn below:
(i) ∠C = 180o – 110o (linear pair)
⇒ ∠C = 70o
We know, ∠A + ∠B + ∠C = 180
⇒ x + 30 + 70 = 180
⇒ x + 100 = 180
⇒ x = 180 – 100
⇒ x = 80o
(ii) ∠PQR = x = 180o – ∠PQS (linear pair)
⇒ x = 180 – 115
⇒ x = 65o
Therefore, ∠PQR + ∠PRQ + ∠RPQ = 180
⇒ 65 + 65 + y = 180
⇒ y + 130 = 180
⇒ y = 180 – 130
⇒ y = 50o
(iii) ∠MYZ = 180o – ∠MYX (linear pair)
⇒ ∠MYZ = 180o – 110o = 70o
Then, 2x + 3x + 70 = 180
⇒ 5x + 70 = 180
⇒ 5x = 180 – 70
⇒ 5x = 110
⇒ x = 22
Therefore, x = 22o, 2x = (2 × 22) = 44o and 3x = (3 × 22) = 66o
(8) Classify the following triangles according to angle:
(i) It has an obtuse angle of 120o. So, it is an obtuse angled triangle.
(ii) All the angle is less than 90o. So it is an acute angled triangle.
(iii) ∠MNL = 90o and sum of its other two acute angle is 90o. So, it is a right angled angle.
(9) Classify the following triangles according to side:
(i) Two sides are equal. So, it is an isosceles triangle.
(ii) All the sides are unequal. So, it is a scalene triangle.
(iii) All the sides are unequal. So, it is a scalene triangle.
(iv) Three sides are equal. So, it is an equilateral triangle.