Quadrilateral Angles Ratio Problem

The sum of the interior angles of any quadrilateral is always 360 degrees. We are given that the angles are in the ratio 1 : 2 : 3 : 4.

Calculating the Angles

Let the angles be represented by $x$, $2x$, $3x$, and $4x$, according to the given ratio. Using the property that the sum of the angles is 360 degrees, we can set up the equation:

$x + 2x + 3x + 4x = 360^\circ$

Combining the terms on the left side gives:

$10x = 360^\circ$

To find the value of $x$, we divide both sides by 10:

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

$x = 36^\circ$

Finding the Greatest Angle

Now that we have the value of $x$, we can find the measure of each angle:

• First angle: $x = 36^\circ$
• Second angle: $2x = 2 \times 36^\circ = 72^\circ$
• Third angle: $3x = 3 \times 36^\circ = 108^\circ$
• Fourth angle: $4x = 4 \times 36^\circ = 144^\circ$

The greatest of these angles is the one corresponding to the largest part of the ratio, which is $4x$.

The greatest angle is $4x = 144^\circ$.