Which one of the following cannot be the ratio of angles in a right-angled triangle?
Explanation:
The largest angle in a right-angled triangle is 90º, which corresponds to the highest part of the ratio. Let us evaluate each option.
Option (a): Angles will be x, 2x and 3x ∴ x + 2x + 3x = 180° ⇒ x = 30° and 3x = 90° Hence, option (a) is correct.
Option (b): Angles will be x, x and 2x ∴ x + x + 2x = 180° ⇒ x = 45° and 2x = 45° Hence, option (b) is correct.
Option (c): Angles will be x, 3x and 6x ∴ x + 3x + 6x = 180° ⇒ x = 18° and neither 3x nor 6x = 90° Hence, option (c) is not a right triangle.
Hence, option (c).
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