What is the sum of an interior angle and its adjacent exterior angle?
Ummmhhh, wouldn't they form a straight line? So ...
draw a triangle and extend the sides.
It should be clear that the two angles form a straight line.
So, ...
180?
To find the sum of an interior angle and its adjacent exterior angle, we first need to understand the relationship between these angles in a polygon.
In any polygon, the sum of an interior angle and its adjacent exterior angle always adds up to 180 degrees.
Here's how you can understand this relationship:
1. Start by drawing a polygon. Let's say we have a triangle for simplicity.
2. Label one of the interior angles as "x." This will be the angle you want to find the sum for.
3. The adjacent exterior angle to the interior angle "x" is the angle formed by extending one of the sides of the polygon. In this case, it will be the angle formed by extending one side of the triangle.
4. Label the adjacent exterior angle as "y."
5. Now, find the sum of angle "x" and angle "y." You will notice that when you add these angles, they will always equal 180 degrees, regardless of the size or shape of the polygon.
This relationship holds true for all types of polygons, whether it's a triangle, square, pentagon, or any other polygon.
So, the sum of an interior angle and its adjacent exterior angle in any polygon is always 180 degrees.