Question

The angles in triangle are in the ratio of 2:2:4. Find the exterior angle adjacent to the largest angle.

Answer 1

The sum of all interior angles in a triangle is 180°.

the angles in this triangle are on a 2:2:4, we know if we add all those three angles, we'd end up with 180°, therefore then 180 is on a 2:2:4 ratio.

in other words, 180 divided by (2+2+4) gives us  22.5°.

now, we know one angle takes 2 of those 22.5, so is 22.5+22.5 or 45°.

the other angle takes the same 2 of those, so is also 45°.

and the largest one takes 4 of those, so is 22.5(4) or 90°.

now, what's the exterior angle to a 90°  angle?  check the picture below.