Respuesta :

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.
Ver imagen jdoe0001

The exterior angle adjacent to the largest angle is 90°.

Given to us,

The ratio of the angles, 2:2:4,

Let the angles be 2x, 2x, and 4x, which are in the same ratio as given in the question.

We know that sum of all angles of a triangle is 180

[tex]2x + 2x + 4x = 180^o\\8x = 180^o\\\\x = \dfrac{180}{8} \\\\x= 22.5[/tex]

Subsituting the value of in angle,  2x, 2x, and 4x,

2x = 2 x 22.5 = 45°,

2x = 2 x 22.5 = 45°,

4x = 4 x 22.5 = 90°,

Therefore, the exterior angle adjacent to the largest angle,

180 - largest angle = exterior angle adjacent

exterior angle adjacent = 180° - 90° = 90°

Hence, the exterior angle adjacent to the largest angle is 90°.

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https://brainly.com/question/2125016