A triangle has three internal angles in the ratio of 3 : 4 : 5. What is the value of the greatest external angle?
Explanation:
Sum of the interior angles of a triangle is 180°.
These angles are in the ratio 3 : 4 : 5.
∴ 3x + 4x + 5x = 180°
∴ x = 15°
∴ We get the three angles as 45°, 60° and 75° respectively.
The greatest external angle should be supplementary to the smallest internal angle which measures 45°.
∴ Measure of the greatest external angle = 180 − 45° = 135°
Hence, option (c).
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