Question

If the angles of a quadrilateral are in ap whose common difference is 10° , then the angles of quadrilateral are

Answer 1

Answer:

Required angles of the quadrilateral are 75° , 85° , 95° and 105°.

Step-by-step explanation:

It is given that the angles of the quadrilateral are in AP with the common difference of 10, so the let the smallest angle be a,

Thus,

Let the required angles of the quadrilateral are : a , a + d , a + 2d , a + 3d. where d is the common difference, and in the question it is given that the common difference between the angles is 10.

So,

Let the required angles are a, a + 10, a + 2( 10 ) , a + 3( 10 ).

From the properties of quadrilateral, we know : -

Sum of all angles = 360°

Therefore,

= >  a + ( a + 10 ) + { a + 2( 10 ) } + { a + 3( 10 ) } = 360

= >  a + a + 10 + a + 20 + a + 30 = 360

= >  a + a + a + a + 10 + 20 + 30 = 360

= >  4a + 60 = 360

= >  4a = 300

= >  a = 300 / 4

= >  a = 75

Hence, angles of the quadrilateral are :

first angle = a = 75°

second angle = a + d = ( 75 + 10 )° = 85°

third angle = a + 2d = ( 75 + 20 )° = 95°

fourth angle = a + 3d = ( 75 + 30 )° = 105°

Therefore, angles of the quadrilateral are 75° , 85° , 95° and 105°.