Geometry Fundamentals

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 360360 degrees, which is also written as 360.360^\circ.

What is the measure of a half turn?

Angle Hunt

               

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 360360 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?

Angle Hunt

               

If this fan of angles adds up to a half turn, what is the value of x?x?

Angle Hunt

               

Which value is the largest?

Angle Hunt

               

What can we say about xx and y,y, the measures of a vertical pair of angles?

Angle Hunt

               

A "quarter turn" gets a special name. We call it a right angle, and it has a measure of 90.90^\circ. In diagrams, 90 degree angles are sometimes identified with a small square block instead of a circle-wedge.

Angle Hunt

               

What is the value of x?x?

Angle Hunt

               

Now let's combine using everything that's been introduced so far.

What is the measure of the unknown angle?

Angle Hunt

               
×

Problem Loading...

Note Loading...

Set Loading...