Answer:
The largest angle of the quadrilateral is 120°.
Step-by-step explanation:
Given : The ratio of three consecutive angles in a cyclic quadrilateral is 2:3:4
To find : The largest angle of the quadrilateral, in degrees ?
Solution :
Let the ration be 'x',
So, The consecutive angles are 2x , 3x and 4x.
We know that, Opposite angles of cyclic quadrilateral is 180°.
i.e. [tex]2x+4x=180[/tex]
[tex]6x=180[/tex]
[tex]x=\frac{180}{6}[/tex]
[tex]x=30[/tex]
The angles became,
[tex]2x=2(30)=60[/tex]
[tex]3x=3(30)=90[/tex]
[tex]4x=4(30)=120[/tex]
We know that sum of all angles of quadrilateral is 360°,
Let the fourth angle be A,
[tex]A+60+90+120=360[/tex]
[tex]A+270=360[/tex]
[tex]A=360-270[/tex]
[tex]A=90[/tex]
Therefore, Among all the angles the largest angle of the quadrilateral is 120°.
