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Question
The interior angles of a triangle are in the ratio 1:2:3, then the ratio of its exterior angles is 3:2:1.
Options
True
False
Solution
This statement is False.
Explanation:
Given, ratio of interior angles = 1:2:3
Let the interior angles be x, 2x and 3x.
So, x + 2x + 3x = 180° ...[Angle sum property of triangle]
⇒ 6x = 180°
⇒ x = `180^circ/6` = 30°
∴ The interior angles are 30°, 60° and 90°.
Now, the exterior angles will be (180° – 30°), (180° – 60°) and (180° – 90°), i.e. 150°, 120° and 90°.
The ratio of exterior angles = 150° : 120° : 90°
= 15 : 12 : 9
= 5 : 4 : 3
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