Question

three angles of a quadrilateral are in the ratio 3 is to 2 is to 1 the sum of the smallest and greatest angle is 180 degree find the all angles of a quadrilateral

Answer 1

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

Let the angles be: [math]\angle A,\angle B,\angle C and\angle D.[/math]

[math]\angle A+\angle B+\angle C+\angle D=360°[/math]

Let the common ratio be[math]x[/math], and then let [math]\angle A:\angle B:\angle C=4x:5x:6x[/math]

Also, let [math]\angle D=y[/math]

[math]\Rightarrow \angle A+\angle B+\angle C+\angle D=4x+5x+6x+y=360°[/math]

[math]\Rightarrow y=360°- 15x. (1)[/math]

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:

[math]\Rightarrow [/math][math]4x[/math][math] + 6x =160°.[/math]

[math]\Rightarrow x=16[/math]

[math]\Rightarrow[/math][math]\angle A=4x=4*16=64°[/math]

[math]\angle B=5x=5*16=80°[/math]

[math]\angle C=6x=6*16=96° [/math]

[math]\angleD= y =360°-15x =360°-15*16=360-240°=120°[/math]

Happy math!!

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