NCERT Solution class 7 Mathematics EXERCISE- 6.3
CHAPTER – 6
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