Many geometric techniques and solutions hinge on finding the measures of a shape's angles.
It'll be helpful to think of an angle as the measure of a turning motion or rotation. When we use the unit of degrees to measure angles, one full turn is defined to measure exactly degrees, which is also written as
What is the measure of a half turn?
If you've already taken a geometry class somewhere, you might have been asked to memorize that these little angles created by extending the edges of any polygon will always add up to exactly degrees.
But, if you think about angles as a "turning" motion, you can really see and understand why that's true.
Using this observation, what is the measure of the the pink-shaded angle in the figure?
If this fan of angles adds up to a half turn, what is the value of
Which value is the largest?
What can we say about and the measures of a vertical pair of angles?
A "quarter turn" gets a special name. We call it a right angle, and it has a measure of In diagrams, 90 degree angles are sometimes identified with a small square block instead of a circle-wedge.
What is the value of
Now let's combine using everything that's been introduced so far.
What is the measure of the unknown angle?