The sides of a triangle are in the ratio 3 : 4 : 5. The measure of the largest angle of the triangle is

### Concept & Angle Sum Property *Note: The original question text contains a typographical error, stating "sides" instead of "angles". A triangle with sides in the ratio 3:4:5 is a right-angled triangle with the largest angle being 90°, which is not among the given options. To match the provided options, we must solve under the assumption that the "angles" are in the ratio 3:4:5.* The sum of all interior angles of a triangle is always 180°. ### Step-by-Step Solution * Assume the angles of the triangle are $3x$, $4x$, and $5x$. * By the angle sum property of a triangle: $3x + 4x + 5x = 180^\circ$. * $12x = 180^\circ$ * $x = \frac{180^\circ}{12} = 15^\circ$ * The largest angle corresponds to the largest ratio part, which is $5x$. * Largest angle = $5 \times 15^\circ = 75^\circ$. ### Exam Strategy & Shortcut Recognize that the total ratio parts are $3 + 4 + 5 = 12$. Divide the total sum of angles, 180°, by 12 to find the value of one ratio unit ($15^\circ$). Instantly multiply by the largest ratio unit (5) for the largest angle: $15 \times 5 = 75^\circ$. ### Common Pitfall Misinterpreting the ratio as sides literally and concluding the triangle is a right triangle. This would lead to an answer of 90°, confusing the student when it does not appear in the multiple-choice options due to the book's misprint. ### Final Answer Therefore, the correct answer is **75°**.