Question

If the angles of a quadrilateral are (2x+10),(3x+15),(2x-10)and(3x-5) the measure of it greatest angle is

Answer 1

Answer:

We know,

= > sum of all angles of any quadrilateral = 360

Here,

= > ( 2x + 10 ) + ( 3x + 15 ) + ( 2x - 10 ) + ( 3x - 5 ) = 360

= > 2x + 10 + 3x + 15 + 2x - 10 + 3x - 5 = 360

= > 2x + 3x + 2x + 3x +10 + 15 - 10 - 5 = 360

= > 10x + 10 = 360

= > 10x = 360 - 10

= > x = 350/10

= > x = 35

On observing I found the greatest angle is 3x + 15, so

= > 3( 35 ) + 15

= > 105 + 15

= > 120

Greatest angle is 120

Answer 2

Sum of all angles of any quadrilateral = 360

= ( 2x + 10 ) + ( 3x + 15 ) + ( 2x - 10 ) + ( 3x - 5 ) = 360

=  2x + 10 + 3x + 15 + 2x - 10 + 3x - 5 = 360

= 2x + 3x + 2x + 3x +10 + 15 - 10 - 5 = 360

= > 10x + 10 = 360

= > 10x = 360 - 10

= > x = 350/10

= > x = 35

The greatest angle is 3x + 15, so

= 3( 35 ) + 15

= 105 + 15

= 120

The greatest angle is 120