The angles of a quadrilateral are in the ratio of 1 : 2 : 3 : 4. What is the measure of the greatest of these angles?

Correct option is A

Given:

The angles of a quadrilateral are in the ratio of 1 : 2 : 3 : 4.
We are to find the measure of the greatest of these angles.

Formula Used:

Sum of interior angles of a quadrilateral=$$360^\circ$$​

Solution:

$$x + 2x + 3x + 4x = 360^\circ$$​​

​$$10x = 360^\circ$$​

​$$x = \frac{360^\circ}{10} = 36^\circ$$​

Now, the angles are:

x = $$36^\circ$$​​

2x$$= 72^\circ$$​​

3x$$= 108^\circ$$​​

4x $$= 144^\circ$$​​

The greatest angle is $$144^\circ.$$​​