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 :)
