## MP Board Class 7th Maths Solutions Chapter 6 The Triangles and Its Properties Ex 6.3

Question 1.

Find the value of the unknown x in the following diagrams:

Solution:

The sum of all interior angles of a triangle is 180°. By using this property, these problems can be solved as follows :

(i) x + 50° + 60° = 180°

⇒ x +110° = 180°

⇒ x = 180° -110° = 70°

(ii) x + 90° + 30° = 180°

⇒ x + 120° = 180°

⇒ x = 180° – 120° = 60°

(iii) x + 30° + 110° = 180°

⇒ x + 140° = 180°

⇒ x = 180° – 140° = 40°

(iv) 50° + x + x = 180°

⇒ 2x = 180° – 50° = 130°

(v) x + x + x = 180°

⇒ 3x = 180°

(vi) x + 2x + 90° = 180°

⇒ 3x = 180° – 90° = 90° = 90°

Question 2.

Find the values of the unknowns x and y in the following diagrams:

Solution:

(i) y + 120° = 180° (Linear pair)

⇒ y = 180° – 120° = 60°

Now, x + y + 50° = 180°

(Angle sum property)

⇒ x + 60° + 50° = 180° x = 180° – 60° – 50° = 70°

(ii) y = 80° (Vertically opposite angles)

Now, y + x + 50° = 180°

(Angle sum property)

⇒ 80° + x + 50° = 180°

⇒ x = 180° – 80°- 50° = 50°

(iii) y + 50° + 60° = 180°

(Angle sum property)

⇒ y = 180° – 60° – 50° = 70°

Now, x + y = 180° (Linear pair)

⇒ x = 180° – y = 180° – 70° = 110°

(iv) x = 60° (Vertically opposite angles)

Now, 30° + x + y = 180°

(Angle sum property)

⇒ 30° + 60° + y = 180° y = 180° – 30° – 60° = 90°

(v) y = 90° (Vertically opposite angles)

Now, x + x + y = 180°

(Angle sum property)

⇒ 2x + 90° = 180°

⇒ 2x = 180° – 90° = 90°

(vi) y = x (Vertically opposite angles)

a = x (Vertically opposite angles)

b = x (Vertically opposite angles)

Now, a + b + y = 180°

(Angle sum property)

⇒ x + x + x= 180°

⇒ 3x = 180°

Hence, y = x = 60°