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Describe two ways that an exterior angle of a triangle is related to one or more of the interior angles.

Sagot :

the 2 angles at a vertex are supplementary (one interior and one exterior) the exterior angle is = the the sum of the 2 remote interior angles hope this helps
Louli

Answers:

1- An exterior angle and its adjacent one are supplementary

2- The measure of the exterior angle is equal to the summation of the other two non-adjacent interior angles

Explanation:

Please refer to the attached image

Part 1:

In the given triangle, consider angles 3 and 4.

Now, these two angles are adjacent and form a linear pair. This means that their summation is 180° which means that they are supplementary angles.

We can also note that angle 3 is an interior angle of the triangle while angle 4 is an exterior angle of the triangle.

Therefore, we can conclude that:

An exterior angle and its adjacent one are supplementary

Part 2:

We know that:

1- sum of angles of a triangle is 180°. Therefore:

angle 1 + angle 2 + angle 3 = 180°

2- angle 3 and angle 4 are supplementary angles. Therefore:

angle 3 + angle 4 = 180°

angle 3 = 180 - angle 4

We can now rewrite the sum of angles of a triangle as follows:

angle 1 + angle 2 + 180 - angle 4 = 180

Now, we solve as follows:

angle 1 + angle 2 - angle 4 = 0

angle 1 + angle 2 = angle 4

Since:

angles 1 and 2 are interior angles of the triangle and are non-adjacent to the exterior angle

angle 4 is an exterior angle of the triangle

Therefore, we can conclude that:

The measure of the exterior angle is equal to the summation of the other two non-adjacent interior angles

Hope this helps :)

View image Louli
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