The interior angles of a triangle are in the ratio 1:2:3, then the ratio of its exterior angles is 3:2:1. State whether the statement is true or false.
Solution:
Given, The interior angles of a triangle are in the ratio 1:2:3, then the ratio of its exterior angles is 3:2:1
We have to determine if the given statement is true or false.
Let the angles be x, 2x and 3x.
By angle sum property, the sum of all the interior angles of a triangle is equal to 180 degrees.
So, x + 2x + 3x = 180°
6x = 180°
x = 180°/6
x = 30°
Now, 2x = 2(30°) = 60°
3x = 3(30°) = 90°
We know, exterior angle = 180° - interior angle
(i) when interior angle is 30 degrees
Exterior angle = 180° - 30° = 150°
(ii) when interior angle is 60 degrees
Exterior angle = 180° - 60° = 120°
(iii) when interior angle is 30 degrees
Exterior angle = 180° - 90° = 90°
Required ratio = 150 : 120 : 90
= 15 : 12 : 9
= 5 : 4 : 3
Therefore, the ratio of exterior angles is 5:4:3
✦ Try This: The interior angles of a triangle are in the ratio 3:2:1, then the ratio of its exterior angles is 4:5:3. State whether the statement is true or false.
☛ Also Check: NCERT Solutions for Class 8 Maths
NCERT Exemplar Class 8 Maths Chapter 5 Problem 108
The interior angles of a triangle are in the ratio 1:2:3, then the ratio of its exterior angles is 3:2:1. State whether the statement is true or false.
Summary:
The given statement ”The interior angles of a triangle are in the ratio 1:2:3, then the ratio of its exterior angles is 3:2:1” is false.
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