Question

The measures of the angles in a triangle are in the ratio of 2:2:4. Find the exterior

Answer 1

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.

$2x+2x+4x=180^\circ$

$8x=180^\circ$

$x=\dfrac{180^\circ}{8}$

$x=22.5^\circ$

Clearly, x=22.5>1, so 4x is the largest angle between 2x, 2x and 4x.

Now,

$\text{Largest angle}=4x$

$\text{Largest angle}=4(22.5^\circ)$

$\text{Largest angle}=90^\circ$

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.

$\text{Largest angle}+y=180^\circ$

$90^\circ+y=180^\circ$

$y=180^\circ-90^\circ$

$y=90^\circ$

Therefore, the exterior  angle that is adjacent to the largest angle is 90°.