Angle types and pairs
Angles rarely appear alone. What does an arrangement of two of them force to be true?
Where you are 8 inside
What this area is about
A single angle is just a number of degrees. Almost everything useful about angles comes from how two of them sit together: sharing an edge, sharing a vertex, or lying along one straight line. Certain arrangements force certain measures, and that is what lets you find an angle you were never told.
How these fit together
Names and tools. Acute, right, obtuse and straight angles sort angles by size, with nothing to prove. Congruent angles, angle addition and bisectors says when two angles match, how measures add when an angle is split, and what a bisector does. Perpendicular lines name the square crossing.
Measure pairs. Complementary and supplementary angles are defined by their measures alone, adding to 90^\circ or 180^\circ, wherever the two angles are drawn.
Arrangements. Adjacent angles and linear pairs and vertical angles each describe how two angles can sit, with a fact about their measures. Vertical angles also holds finding unknown angle measures, which chains all of these: the star to aim at.
A path through it
Sizes, congruent angles and perpendicular lines first. Then complementary and supplementary angles, adjacent angles and linear pairs, and last vertical angles and the chase.
Most results here come from three numbers: a right angle is 90^\circ, a straight line 180^\circ, a full turn 360^\circ.
Finish here and you can work out unmarked angles from the ones you are given. Triangles, parallel lines and transversals and every proof about angle pairs assume it.