Basic Angle Properties
What are the basic angle properties?
- Angles that meet at a point add up to 360°
- Angles that meet at a point on a straight line add up to 180°
- Vertically opposite angles are equal
- Vertically opposite angles occur when two lines intersect
- They are the angles either side of the intersection that are opposite to each other
What are the angle properties with triangles?
- The three interior angles inside any triangle add up to 180°
- If the triangle is isosceles then two angles will be equal
- These will be the two angles opposite the two sides of equal length
- If the triangle is equilateral then the three angles will be equal
- Each angle will equal 60°
What are the angle properties with quadrilaterals?
- The four interior angles inside any quadrilateral add up to 360°
- If the quadrilateral is a square or a rectangle then all the angles are equal
- Each angle will equal 90°
- You can use any symmetries of the quadrilateral to identify other equal angles
- For a parallelogram or rhombus opposite angles are equal
- For a kite one pair of opposite angles are equal
Examiner Tip
- Find all the missing angles that you can using the angles that are given to you in a question
- They might not seem to help you straight away but having more angles will lead you to find the angle you need
Worked example
The diagram below is formed by three straight lines. Find the value of .
Label the other missing angles inside the triangle.
Vertically opposite angles between two intersecting lines are equal.
Angles that meet on a straight line add up to 180°.
Interior angles in a triangle add up to 180°.