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Given:
The measures of the angles in a triangle are in the ratio of 2:2:4.
To find:
The exterior angle that is adjacent to the largest angle.
Solution:
Let the interior angles of the triangle are 2x, 2x and 4x respectively.
According to the angle sum property, the sum of interior angles of a triangle is 180 degrees.
Clearly, x=22.5>1, so 4x is the largest angle between 2x, 2x and 4x.
Now,
Let the required exterior angle that is adjacent to the largest angle be y.
Interior angle and adjacent exterior angles are supplementary, so their sum is 180 degrees.
Therefore, the exterior angle that is adjacent to the largest angle is 90°.