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Hong Kong
Stage 1 - Stage 3

Exterior Angle Sum and other Calculations

Lesson

Exterior angle in a triangle

Lets have a look at the triangle image above. 

What relationships do we know exist?

We know that $y+z=180$y+z=180, because Adjacent angles on a straight line are supplementary (they add up to $180$180 degrees).

We also know that $w+x+y=180$w+x+y=180 because The angle sum of a triangle is $180$180 degrees.

Since both of these equations sum to $180$180, we know that they are both equal. This means that we have

$y+z=w+x+y$y+z=w+x+y.

Subtracting $y$y from both sides of the equation gives us the result

$z=w+x$z=w+x.

Have a look at where these angles are positioned on the triangle. 

This special relationship is used frequently in solving geometrical problems. We say formally that the: exterior angle of a triangle is equal to the sum of the two opposite interior angles. Can you see how this statement is a descr