# The sum of the measures of two exterior angles of a triangle is 255. What is the measure of the third?

Apr 13, 2018

The third external angle is: ${105}^{o}$

#### Explanation:

$\textcolor{b l u e}{\text{Preliminary thinking - preparing to tackle the question}}$

At any vertex the: exterior angle + internal angle $= {180}^{o}$

So for 3 vertices this sum is $3 \times {180}^{o} = {540}^{o}$

It is known that the sum if the internal angles is ${180}^{o}$

so $\textcolor{b r o w n}{\text{the sum of the external angles is: } {540}^{o} - {180}^{o} = {360}^{o}}$
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$\textcolor{b l u e}{\text{Answering the question}}$

We have two vertices and we are told the sum of their external angles is ${255}^{o}$

So the third external angle is ${360}^{o} - {255}^{o} = {105}^{o}$