The three angles of a triangle are in the ratio $2 : 3 : 4$ . What is the largest angle?

60^\circ

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72^\circ

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80^\circ

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90^\circ

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Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

The angles of any triangle add to $180^\circ$ .
The ratio has $2 + 3 + 4 = 9$ parts, so one part is $180^\circ \div 9 = 20^\circ$ .
The largest angle has 4 parts: $4 \times 20^\circ = 80^\circ$ .
Check: $40^\circ + 60^\circ + 80^\circ = 180^\circ$ .

Worth noting

The largest angle is under $90^\circ$ , so this is an acute-angled triangle. The $90^\circ$ on offer assumes a ratio like this must produce a right angle; it does not.

Concept: Angle sum of a triangle with angles in a ratio
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The three angles of a triangle are in the ratio 2:3:42 : 3 : 42:3:4. What is the largest angle?

Explanation

The three angles of a triangle are in the ratio $2 : 3 : 4$ . What is the largest angle?