Angles are measured in degrees and are a measure of the turn between two lines that meet at a point. Let’s have a look at some properties of triangles, circles, and quadrilaterals that may help.
The sum of the interior angles of a triangle is always 180 degrees.
Example: Given a triangle with angles \(\angle A = 50^\circ\) and \(\angle B = 60^\circ\) , find \(\angle C\).
The sum of the interior angles of a quadrilateral is always 360 degrees.
Example: Given a quadrilateral with angles \(\angle F = 90^\circ\), \(\angle G = 85^\circ\), and \(\angle H = 95^\circ\), find \(\angle I\).
The sum of the angles on a straight line is always 180 degrees.
Example: If \(\angle D = 120^\circ\), find \(\angle E\) on the same straight line.
The sum of the angles around a point (or in a circle) is always 360 degrees. This is because a circle represents a full rotation.
Example: If three angles around a point are \(100^\circ\), \(120^\circ\), and \(80^\circ\), find the fourth angle \(\angle J\).
In an isosceles triangle, two of the angles are equal. This is because two sides of the triangle are of equal length, leading to two equal angles opposite those sides.
Example: Given an isosceles triangle with \(\angle K = 40^\circ\) and the two equal angles \(\angle L\) , find \(\angle L\) .