What do you notice about the measure of the exterior angle and its adjacent interior angle?
Question: What do you notice about the measure of the exterior angle and its adjacent interior angle?
The measure of an exterior angle and its adjacent interior angle in a polygon always add up to 180 degrees. This is because they form a linear pair, which are supplementary angles.
A linear pair is a pair of adjacent angles formed when two lines intersect. Here are some key points about linear pairs:
- Adjacent Angles: The two angles share a common vertex and a common side.
- Supplementary Angles: The measures of the two angles add up to 180 degrees.
- Straight Line: The non-common sides of the angles form a straight line.
For example, if two angles form a linear pair and one angle measures 70 degrees, the other angle will measure 110 degrees because (70^\circ + 110^\circ = 180^\circ).
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