Basic angle rules
In a nutshell
There are five rules involving angles on lines and shapes. These rules refer to angles in a triangle, angles on a straight line, angles in a quadrilateral, angles around a point and angles in an isosceles triangle. The rules help to find missing angles on lines and in shapes.
Angles in a triangle
The angles in a triangle add up to 180°.
Example 1
Find the size of the missing angle in the triangle:
Angles in a triangle add up to 180°.
70°+30°180°−100°=100°=80°
The missing angle is 80°.
Angles on a straight line
Angles on a straight line add up to 180°.
Example 2
Find the size of the missing angle on the straight line:
Angles on a straight line add up to 180°.
180°−100°=80°
The missing angle is 80°.
Angles in a quadrilateral
Angles in a quadrilateral add up to 360°.
Example 3
Find the size of the missing angle in the quadrilateral shown:
Angles in a quadrilateral add up to 360°. Subtract the sum of the known angles from 360°.
80°+120°+40°360°−240°=240°=120°
The missing angle is 120°.
Angles around a point
Angles around a point add up to 360°.
Example 4
Find the size of the missing angle:
Angles around a point add up to 360°, so take 140° away from 360°.
360°−140°=220°
The missing angle is 220°.
Angles in an isosceles triangle
Isosceles triangles have two sides equal in length and two equal angles. The two equal angles are sometimes referred to as the 'base angles' in an isosceles triangle. If you know one of the angles in an isosceles triangle, the other two angles can be found easily.
Example 5
The isosceles triangle has equal sides AC and BC. If ∠BAC is 50°, find the size of ∠ACB.
∠BAC and ∠ABC are both 50°, as they are the base angles of the triangle. As angles in a triangle add up to 180°, you can find ∠ACB by subtracting the sum of ∠ABC and ∠BAC from 180°.
50°+50°180°−100°=100°=80°
∠ ACB =80°