Angle facts at a point

An angle measures a turn. A right angle is \(90^\circ\), a straight angle is \(180^\circ\), and a complete turn is \(360^\circ\). Acute angles lie between \(0^\circ\) and \(90^\circ\); obtuse angles between \(90^\circ\) and \(180^\circ\); reflex angles between \(180^\circ\) and \(360^\circ\).

Adjacent angles on a straight line total \(180^\circ\). Angles around a point total \(360^\circ\). When two straight lines intersect, vertically opposite angles are equal because each is supplementary to the same adjacent angle.

Example

Two intersecting straight lines form an angle of \(67^\circ\). Its vertically opposite angle is \(67^\circ\); each adjacent angle is \(180^\circ-67^\circ=113^\circ\). The four angles total \(360^\circ\).

Complementary angles total \(90^\circ\); supplementary angles total \(180^\circ\). These words describe sums and do not require the angles to be adjacent.