Question

The angles of a quadrilateral are in A.P.If the greatest angle is 165degree,find the measures of the remaining three angles.

The difference of two no's is 4 and their product is 192.Find the no's.

Pls solve as quickly as possible.PLEASE!!!!!!!!!!!

Answer 1

1. let the angles be a, a+d, a+2d and a+3d

given that largest angle is 165
thus a+3d = 165
⇒ a = 165-3d

sum of all angles = 360
⇒ a + a+d + a+2d + a+3d = 360
⇒ 4a + 6d = 360
⇒ 4(165-3d) + 6d = 360
⇒ 660 - 12d + 6d = 360
⇒ -6d = 360-660 = -300
⇒ d = (-300)/(-6) = 50
a = 165 - 3d = 165 -3×50 = 165 - 150 = 15
a+d = 15+50 = 65
a+2d = 15+50×2 = 15+100 = 115

So all angles are 15, 65, 115 and 165.

2.difference between two numbers is 4
let smaller number is x
other number = x+4

product = 192 
⇒x(x+4) = 192
⇒x² + 4x -192 = 0
⇒ x² + 16x -12x - 192 = 0
⇒ x(x+16)-12(x+16) = 0
⇒ (x+16)(x-12) = 0
⇒ x = 12 or -16
when x=12, x+4 = 12+4 = 16
when x = -16, x+4 = -16+4 = -12
So the numbers are (12 and 16) and (-12 and -16)