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An exterior angle of a triangle is 800 and the interior opposite angles are in the ratio 1 : 3. Measure of each inte4rior opposite angle is :
  • a)
    200, 600
  • b)
    400, 1200
  • c)
    300, 600
  • d)
    300, 900
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
An exterior angle of a triangle is800and the interior opposite angles ...
Correct answer is a.
If exterior angle is 80, then the interior angle is
180-80=100
Sum of the interior angles of triangle is 180. If opposite angle is in ratio 1:3 then to gain the sum of 180. the angles must be 20 and 60. Because
100+20+60=180.
If it would be 40, 120 then the sum will be 100+40+120=260 which is not equal to180. If it would be 30, 60 then the sum will be 100+30+60=190 which is not equal to 180.
If it would be 30, 90 then the sum will be 100+30+90=220 which is not equal to 180.
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Community Answer
An exterior angle of a triangle is800and the interior opposite angles ...
Let the interior angles be x and 3x 
We know that exterior angle of triangle is equal to sum of interior opposite angles.
⇒ x+3x=80
⇒ 4x=80
⇒ x=20
So the angles are 
x=20
3x=3×20
= 60∘
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