Angles at a point and on a straight line

Angles at a point

Angles around a point add up to 360°. This fact can be used to calculate missing angles.

Example

Calculate angle \(a\).

360 degrees, split into 60, 95 and 105 degrees, plus unknown angle, a

\[a = 360^\circ - 60^\circ - 95^\circ - 105^\circ = 100^\circ\]

Angles on a straight line

Angles on a straight line add up to 180°. This fact can also be used to calculate angles.

Example

Calculate the angles \(b\) and \(c\).

Intrersecting lines, showing known angle of 30 degrees, plus unknown angles, b and c

\[b = 180^\circ - 30^\circ = 150^\circ\]

\[c = 180^\circ - 150^\circ = 30^\circ\]

\(c\) and \(30^\circ\) are called vertically opposite angles.

Vertically opposite angles are equal.