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kenny6666 [7]
2 years ago
8

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

Mathematics
1 answer:
scoray [572]2 years ago
3 0

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°.

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