In a convex quadrilateral, one of the interior angles measures 72°. The remaining three interior angles are in the ratio 2 : 3 : 7. Calculate the difference between the largest and the smallest of these three remaining angles.

The correct option is 120°.

Step-by-Step Explanation:

Step 1: Find the sum of the remaining three interior angles.
The sum of all four interior angles in any convex quadrilateral is always equal to 360°.
Given that one of the interior angles measures 72°, the sum of the remaining three interior angles is:

$\text{Sum of remaining angles}=360°-72°=288°$

Step 2: Determine the value of each ratio part.
The remaining three interior angles are given in the ratio 2 : 3 : 7.
Let the common ratio multiplier be $x$.
The three angles are represented as $2x$, $3x$, and $7x$.

Summing these angles:

$2x+3x+7x=288°$

$12x=288°$

$x=\frac{288°}{12}=24°$

Step 3: Calculate the largest and smallest of these three angles.
Smallest angle = $2x=2\times 24°=48°$
Largest angle = $7x=7\times 24°=168°$

Step 4: Find the difference between the largest and smallest angles.
The difference between the largest and the smallest of these three remaining angles is:

$\text{Difference}=168°-48°=120°$

Therefore, the difference between the largest and smallest of these three angles is 120°.