Angles in Triangles (Edexcel IGCSE Maths)

Spec point — 4.1C

Angles in triangles

What are the angle properties of 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 all three angles will be equal

  • Each angle will equal 60°

• A right-angled triangle has one 90° angle

Exam Hint 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 using three straight lines. Find the value of $x$.

Answer:

Label the other missing angles inside the triangle

Vertically opposite angles between two intersecting lines are equal

$y=60$

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

$\begin{gathered} z + 130 & = 180 \\ z & = 50 \end{gathered}$

Interior angles in a triangle add up to 180°

$\begin{gathered} x + 60 + 50 & = 180 \\ x + 110 & = 180 \end{gathered}$

$x=70$