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°
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Correct Answer: 105°
Solution : The angles of a triangle are in the ratio 2 : 3 : 7. Let the angles be 2x , 3x, and 7x. Since the sum of all angles in a triangle is 180°, $\therefore$ 2x + 3x + 7x = 180° ⇒ 12x = 180° $\therefore$ x = 15° Now the angles of the triangle are: 2x = 2 × 15 = 30° 3x = 3 × 15 = 45° 7x = 7 × 15 = 105° So the largest angle of the triangle is 105°. Hence, the correct answer is 105°.
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