Question

The measures of four angles of a quadrilateral are consecutive odd natural numbers. Find out the measures of these angles.​

Answer 1

Answer :-

The angles of the quadrilateral are :-

• 87°
• 89°
• 91°
• 93°

Step-by-step explanation :

To Find :-

• The measure of all the angles of quadrilateral

Solution :-

Given that,

• The measures of four angles of a quadrilateral are consecutive odd natural numbers.

Assumption:

Let us assume the The measures of four angles of a quadrilateral are consecutive odd natural numbers as x, ( x + 2 ), ( x + 4 ) and ( x + 6 ).

As we know that,

Sum of all angles of quadrilateral = 360°

Therefore,

• x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) = 360°

=> x + ( x + 2 ) + ( x + 4 ) + ( x + 6 ) = 360

=> x + x + 2 + x + 4 + x + 6 = 360

=> 4x + 12 = 360

=> 4x = 360 - 12

=> 4x = 248

=> x = 248/4

=> x = 87

• The value of x is 87.

Hence, the angles are :-

The angle which we assumed as x,

=> x

=> 87°

The angle which we assumed as ( x + 2 ),

=> x + 2

=> 87 + 2

=> 89°

The angle which we assumed as ( x + 4 ),

=> x + 4

=> 87 + 4

=> 91°

The angle which we assumed as ( x + 6 ),

=> x + 6

=> 87 + 6

=> 93°

Therefore,

The angles of the quadrilateral are :-

• 87°
• 89°
• 91°
• 93°