Question : The difference between the largest and the smallest angles of a triangle whose angles are in the ratio of 5 : 3 : 10 is:
Option 1: 20°
Option 2: 30°
Option 3: 50°
Option 4: 70°
Correct Answer: 70°
Solution :
Given:
The angles are in the ratio of 5 : 3 : 10.
Let the angles be 5$x$, 3$x$, and 10$x$.
We know, 5$x$ + 3$x$ + 10$x$ = 180°
⇒ 18$x$ = 180°
$\therefore x$ = 10°
Largest angle = 10$x$ = 10 × 10° = 100°
Smallest angle = 3$x$ = 3 × 10° = 30°
Difference = 100°- 30° = 70°
Hence, the correct answer is 70°.
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