Gujarat BoardĀ GSEB Textbook Solutions Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.2 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 7 Maths Chapter 6 The Triangles and Its Properties Ex 6.2

Question 1.

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

Solution:

(i) āµ Interior opposite angles are 50Ā° and 70Ā°.

ā“ Using the exterior angle property of a triangle, we have

[Exterior angle] = [Sum of the interior opposite angles]

or x = 50Ā° + 70Ā° = 120Ā°.

(ii) āµ Interior opposite angles are 65Ā° and 45Ā°.

ā“ Using the relation,

[Exterior angle] = [Sum of the interior opposite angles]

We have x = 65Ā° + 45Ā°

or x = 110Ā°.

(iii) āµ Interior opposite angles are 30Ā° and 40Ā°.

ā“ Using the relation,

[Exterior angle] = [Sum of the interior opposite angles]

We have x = 30Ā° + 40Ā°

or x = 70Ā°.

(iv) āµ The interior opposite angles are 60Ā° and 60Ā°.

ā“ Using the relation,

[Exterior angle] = [Sum of interior opposite angles]

We have x = 60Ā° + 60Ā°

or x = 120Ā°.

(v) āµ The interior opposite angles are 50Ā° and 50Ā°.

ā“ Using the relation,

[Exterior angle] = [Sum of the interior opposite angles]

We have x = 50Ā° + 50Ā°

or x = 100Ā°.

(vi) āµ The interior opposite angles are 30Ā° and 60Ā°.

We have x = 30Ā° + 60Ā°

or x = 90Ā°.

Question 2.

Find the value of the unknown interior angle x in the following figures:

Solution:

(i) Exterior angle =115Ā°

One of the interior opposite angles = 50Ā°

Using the relation,

[Sum of the interior opposite angles] = [Exterior angle]

We have x + 50Ā° = 115Ā°

or x = 115Ā° – 50Ā°

or x = 65Ā°.

Thus, the measure of the unknown interior angle is 65Ā°.

(ii) āµ Exterior angle = 100Ā°

Interior opposite angles are 70Ā° and x.

ā“ Using the relation,

[Sum of the interior opposite angles] = [Exterior angle]

We have 70Ā° + x = 100Ā°

or x = 100Ā° – 70Ā°

or x = 30Ā°

ā“ The required measure of the unknown interior opposite angle is 30Ā°.

(iii) āµ Exterior angle = 125Ā°

Interior opposite angles are 90Ā° and x.

ā“ Using the relation,

[Sum of the interior opposite angles] = [Exterior angle]

We have x + 90Ā° = 125Ā°

or x = 125Ā° – 90Ā° = 35Ā°

Thus, the value of unknown interior opposite angle is 35Ā°.

(iv) āµ Exterior angle = 120Ā°

Interior opposite angles are 60Ā° and x.

ā“ Using the relation,

[Sum of the interior opposite angles] = [Exterior angle]

We have x + 60Ā° = 120Ā°

or x = 120Ā° – 60Ā° = 60Ā°

Thus, the measure of the unknown interior opposite angle is 60Ā°.

(v) āµ Exterior angle = 80Ā°

Interior opposite angles are 30Ā° and x.

ā“ Using the relation,

[Sum of the interior opposite angles] = [Exterior angle]

We have: 30Ā° + x = 80Ā°

or x = 80Ā° – 30Ā° = 50Ā°

Thus, the measure of the unknown interior angle is 50Ā°.

(vi) āµ Exterior angle = 75Ā°

Interior opposite angles are x and 35Ā°.

ā“ Using the relation,

[Sum of the interior opposite angles] = [Exterior angle]

We have x + 35Ā° = 75Ā°

or x = 75Ā° – 35Ā°

or x = 40Ā°

Thus, the measure of the interior opposite angle is 40Ā°.