Question

The ratio of three consecutive angles in a cyclic quadrilateral is $2:3:4$. Find the largest angle of the quadrilateral, in degrees.

Answer 1

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. $2x+4x=180$

$6x=180$

$x=\frac{180}{6}$

$x=30$

The angles became,

$2x=2(30)=60$

$3x=3(30)=90$

$4x=4(30)=120$

We know that sum of all angles of quadrilateral is 360°,

Let the fourth angle be A,

$A+60+90+120=360$

$A+270=360$

$A=360-270$

$A=90$

Therefore, Among all the angles the largest angle of the quadrilateral is 120°.