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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