# EXERCISE – 6.3

Q1. Find the value of the unknown x in the following diagrams:

SOLUTOIN:-

(i) We know that,

The sum of all the interior angles of a triangle is 1800

Then,

= x + 500 + 600 = 1800

= x + 1100  = 1800

= x = 1800 – 1100

= x = 700

(ii) We know that,

The sum of al the interior angles of a triangle is 1800.

The given triangle is a right – angled triangle , So the Angle QPR is 900

= 900 + 300 + x = 1800

= 1200 + x = 1800

= x

= 1800 – 1200

= x = 600

(iii) We know that ,

The sum of interior angles of a triangle  is 1800

= 1100 + 300 + x = 1800

= 1400 + x = 1800

= x = 1800 – 1400

= x = 400

(iv) We know that,

The sum of all the interior angle of a triangle is 1800.

Then,

= 500 + x + x = 1800

= 500 + 2x = 1800

= 2x = 1800 – 500

= 2x = 1300

= x = 1300/2

= x = 650

(v) We know that,

The sum of all interior angles of a triangle is 1800

Then,

= x + x + x = 1800

= 3x = 1800

= x = 1800/3

= x = 600

(vi) We know that,

The sum of all the interior angles of a triangle is 1800.

Then,

= 900 + x + 2x = 1800

= 900 + 3x = 1800

= 3x = 1800 – 900

= 3x = 900

= x = 900/3

= x = 300

Then,

= 2x = 2 x 300 = 600

Q2. Find the values of the unknown x and y in the following diagrams:

SOLUTION:-

(i) We know that,

An exterior angle of a triangle is equal to the sum of its interior opposite angles.

Then,

= 500 + x = 1200

By transposing 500 from LHS to RHS it becomes 500

= x = 1200 – 500

= x = 700

We also know that,

The sum of all interior angles of a triangle is 1800.

Then,

= 500 + x + y = 1800

= 500 + 700 + y = 1800

= 1200 + y = 1800

= y = 1800 – 1200

= y = 600

(ii) From the rule of vertically opposite angles,

= y = 800

Then,

We know that,

The sum of all the interior angles of a triangle is 1800

Then,

We know that,

The sum of all the interior angles of a triangle is 1800

Then,

= 500 + 800 + x = 1800

= 1300 + x = 1800

By transposing 1300 from LHS to RHS it becomes 1300

= x = 1800 – 1300

= x = 500

(iii) We know that,

The sum of all the interior angles of a triangle is 1800

Then,

= 500 + 600 + y = 1800

= 1100 + y = 1800

By transposing 1100 from LHS to RHS it becomes 1100

= y = 1800 – 1100

= y = 700

Now,

From the rule of linear pair,

= x + y = 1800

= x + 700 = 1800

= x = 1800 – 700

= x = 1100

(iv) From the rule of vertically opposite angles,

= x = 600

Then,

We know that,

The sum of all the interior angles of a triangle is 1800

Then,

= 300 + x + y = 1800

= 300 + 600 + y = 1800

= 900 + y = 1800

= y = 1800 – 900

= y = 900

(v) From the rule of vertically opposite angles,

= y = 900

Then,

We know that,

The sum of all the interior angles of a triangle is 1800.

Then,

= x + x + y = 1800

= 2x + 900 = 1800

= 2x = 1800 – 900

= 2x = 900

= x = 900/2

= x = 450

(vi) From the rule of vertically opposite angles,

= x = y

Then,

We know that ,

The sum of all the interior angles of a triangle is 1800

Then,

= x + x + x = 1800

= 3x = 1800

= x = 1800/3

= x = 600