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Question
The angles of a triangle are in the ratio 3 : 1 : 2. The measure of the largest angle is
Options
30°
60°
90°
120°
Solution
90°
The ratio of the angles of a triangle is 3:1:2
Let x be any number such that the three angles are (3x)°, (1x)°, and (2x)°.
We know, the sum of the angles of a triangle is 180°.
3x + 1x + 2x= 180
⇒ 6x = 180
⇒ x = `180/6` = 30
∴ (3x)°= (3 × 30)° = 90°
(1x)° = (1 × 30)° = 30°
(2x)° = (2 × 30)° = 60°
The measure of the largest angle is 90°.
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