Question : The ratio of the angles of a triangle is 2 : 2 : 5. What is the largest angle?
Option 1: $120^\circ$
Option 2: $80^\circ$
Option 3: $110^\circ$
Option 4: $100^\circ$
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Correct Answer: $100^\circ$
Solution :
Let the angles of the triangle be $2x, 2x,$ and $5x$ respectively.
We know that the angles of a triangle are $180^\circ$.
Therefore, by angle sum property:
$2x + 2x + 5x = 180^\circ$
⇒ $9x = 180^\circ$
$\therefore x = 20^\circ$
So, the largest angle $=5\times20^\circ = 100^\circ$
Hence, the correct answer is $100^\circ$.
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