An exterior angle of a triangle is 80° and the interior opposite angles are in the ratio 1:3 Find the measure of interior opposite angles.

Let the interior angles be x and 3x.

We know that the exterior angle of a triangle is equal to the sum of interior opposite angles.

⇒ x + 3x = 80$°$

⇒ 4x = 80$°$

⇒ x = 20$°$

So the angles are:

$\Rightarrow$x = 20$°$

$\Rightarrow$3x = 3 × 20$°$ = 60$°$

Therefore, the interior opposite angles must have a measure of 20^o and 60^o.