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Basic Angle Properties

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

Opposite-Angles

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

Exam 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 x .

3-2-1-cie-igcse-basic-angle-we-diagram

Label the other missing angles inside the triangle.
 

3-2-1-cie-igcse-basic-angle-we-solution-diagram

Vertically opposite angles between two intersecting lines are equal.

y space equals space 60

Angles that meet on a straight line add up to 180°.

table row cell z space plus space 130 space end cell equals cell space 180 space end cell row cell z space end cell equals cell space 50 end cell end table

Interior angles in a triangle add up to 180°.

table row cell x space plus space 60 space plus space 50 space end cell equals cell space 180 space end cell row cell x space plus space 110 space end cell equals cell space 180 end cell end table

bold italic x bold space bold equals bold space bold 70

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