Question

three angles of a quadrilateral are in the ratio 4 :5:6 . the sum of least and the greatest of these is 160 deg. find the angle of quadrilateral.

Answer 1

let all angle be decided by x=4x ,5x, 6x
sum of 4x and 6x =160
sum of all sides it's =180
: 6x+4x+5x =180-----(1)

:5x=20
:4x+6x=160
10x=160
x=160=10
x=16
5x=5*16
4x=4*16
6x=6*16

Answer 2

$\huge\mathfrak\green{Answers}$

The sum of interior angles of a quadrilateral ABCD= 360°

Let the angles be: ∠A,∠B,∠Cand∠D.

∠A+∠B+∠C+∠D=360°

Let the common ratio bex, and then let ∠A:∠B:∠C=4x:5x:6x

Also, let ∠D=y

⇒∠A+∠B+∠C+∠D=4x+5x+6x+y=360°

⇒y=360°−15x.(1)

Assuming that by the sum of largest and smallest angles is 160° (Else the question is insufficient) means it is among the three mentioned angles:

⇒4x+6x=160°.

⇒x=16

⇒∠A=4x=4∗16=64°

∠B=5x=5∗16=80°

∠C=6x=6∗16=96°

D=y=360°−15x=360°−15∗16=360−240°=120°