Key Points

An acute angle measures between $0^\circ$ and $90^\circ$. A right angle is exactly $90^\circ$. An obtuse angle is between $90^\circ$ and $180^\circ$. A straight angle is exactly $180^\circ$, and a reflex angle is between $180^\circ$ and $360^\circ$.

Two angles are complementary if their sum is $90^\circ$. Two angles are supplementary if their sum is $180^\circ$.

Two angles are adjacent if they share a common vertex and a common arm, and their non-common arms are on different sides of the common arm.

A linear pair consists of two adjacent angles whose non-common sides form a straight line. The sum of the angles in a linear pair is always $180^\circ$.

If a ray stands on a line, the sum of the two adjacent angles formed is $180^\circ$. Conversely, if the sum of two adjacent angles is $180^\circ$, their non-common arms form a line.

If two lines intersect each other, then the vertically opposite angles are equal. If lines AB and CD intersect at O, then $\angle AOC = \angle BOD$ and $\angle AOD = \angle BOC$.

The sum of all angles formed around a single point is always equal to $360^\circ$.

Parallel lines are lines that never intersect. A transversal is a line that intersects two or more lines at distinct points, creating various angle pairs.

If a transversal intersects two parallel lines, then each pair of corresponding angles is equal. The converse is also true: if a pair of corresponding angles is equal, the lines are parallel.

If a transversal intersects two parallel lines, then each pair of alternate interior angles is equal. The converse is also true: if a pair of alternate interior angles is equal, the lines are parallel.

If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary (their sum is $180^\circ$). The converse is also true.

Lines which are parallel to the same line are parallel to each other. If line $l \parallel m$ and line $n \parallel m$, then it implies that $l \parallel n$.

The sum of the three interior angles of any triangle is always $180^\circ$. For a triangle $\triangle ABC$, we have $\angle A + \angle B + \angle C = 180^\circ$.

If a side of a triangle is produced, the exterior angle so formed is equal to the sum of the two interior opposite angles.