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°
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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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Question : Possible measures of the three angles of a triangle are:
Option 1: 33°, 42°, and 115°
Option 2: 40°, 70°, and 80°
Option 3: 30°, 60°, and 100°
Option 4: 50°, 60°, and 70°
Question : The sum of two angles of a triangle is 116° and their difference is 24°. The measure of the smallest angle of the triangle is:
Option 1: 38°
Option 2: 28°
Option 3: 46°
Option 4: 64°
Question : The angles of a triangle are in the ratio 2 : 3 : 7. What is the measure of the largest angle of the triangle?
Option 1: 100°
Option 2: 45°
Option 3: 90°
Option 4: 105°
Question : An exterior angle of a triangle is 115° and one of the interior opposite angles is 45°. The other two angles are:
Option 1: 65° and 70°
Option 2: 60° and 75°
Option 3: 45° and 90°
Option 4: 50° and 85°
Question : The ratio of the three sides of the triangle is 5 : 13 : 12. What is the largest angle of the triangle?
Option 1: 80°
Option 2: 90°
Option 3: 135°
Option 4: 120°
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