Answered

At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Join our Q&A platform and get accurate answers to all your questions from professionals across multiple disciplines. Our platform offers a seamless experience for finding reliable answers from a network of knowledgeable professionals.

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
Visit us again for up-to-date and reliable answers. We're always ready to assist you with your informational needs. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.