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

1 Answer
Apr 13, 2018

Answer:

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 #