Question

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

Answer 1

The third external angle is: `105^o`

Explanation:

`color(blue)("Preliminary thinking - preparing to tackle the question")`

At any vertex the: exterior angle + internal angle `=180^o`

So for 3 vertices this sum is `3xx180^o= 540^o`

It is known that the sum if the internal angles is `180^o`

so `color(brown)("the sum of the external angles is: "540^o-180^o=360^o)`
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`color(blue)("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`