In a triangular region, the ratio of two interior angles is 1 : 3. If the measure of the third angle exceeds the sum of the first two angles by 25%, calculate the measure of the largest angle in the triangle.

The correct answer is 100°.

Step-by-step explanation:

Step 1: Express the first two angles in terms of a variable.
The ratio of the first two interior angles is given as 1 : 3.
Let the measure of the first angle be $x$ and the measure of the second angle be $3x$.

Step 2: Find the sum of the first two angles.
$\text{Sum of first two angles}=x+3x=4x$

Step 3: Determine the measure of the third angle.
It is given that the third angle exceeds the sum of the first two angles by 25%.
$\text{Third angle}=4x+(25\%\text{ of }4x)$
$\text{Third angle}=4x+(0.25\times 4x)$
$\text{Third angle}=4x+x=5x$

Step 4: Use the angle sum property of a triangle.
The sum of all three interior angles in any triangle is always 180°.
$x+3x+5x=180°$
$9x=180°$
$x=\frac{180°}{9}=20°$

Step 5: Calculate the measure of each angle and identify the largest one.
1. First angle = $x=20°$
2. Second angle = $3x=3\times 20°=60°$
3. Third angle = $5x=5\times 20°=100°$

Thus, the measure of the largest angle in the triangle is 100°.