Question

three angles of a quadrilateral is in the ratio 4:5:6. The sum of the least and the greatest of these is 160°. Find the angles of the quadrilateral​

Answer 1

Answer

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 = 240

=360−240°=120°

Thanks