Question : The angles of a triangle are in the ratio 1 : 1 : 2. What percentage of the total internal angle is the greatest angle?
Option 1: 50%
Option 2: 65%
Option 3: 45%
Option 4: 40%
Correct Answer: 50%
Solution :
Let the angle of the triangle be x, x, 2x
According to the question,
Sum of angles = 180º
⇒ x + x + 2x = 180º
⇒ 4x = 180º
⇒ x = $\frac{180}{4}$ = 45º
Angles of the triangle are as follows :
⇒ x = 45º
⇒ x = 45º
⇒ Greatest angle = 2x = 2 × 45º = 90º
Now, the percentage of the greatest angle
P = $\frac{90°}{180°}$ × 100
P = $\frac{1}{2} \times100$ = 50%
∴ 50% of the total internal angle is the greatest angle.
Hence, the correct answer is 50%.
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