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An exterior angle is formed between a side and the extension of a side. It will always be a linear pair with an internal angle. In the diagram below, <4 is the exterior angle. The exterior angle theorem states that the external angle is equal to the sum of the two remote angles. The remote angles are those interior angles that are not adjacent to the exterior angle so in this case <1 and <2 are the remote angles.

m<1 + m<2 = m<4, Explain why this is true please !!

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  • HINT: m<1 + m<2 + m<3 = 180 (angle sum in triangle). m<3 + m<4 = 180 (angle sum on straight line) – Mufasa Sep 30 '15 at 21:23
up vote 1 down vote accepted

Angle $1$ + Angle $2$ + Angle $3$ = 180

Angle $3$ + Angle $4$ = 180.

The result is that Angle $4$ = Angle $1$ + Angle $2$.

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