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

Nico Patterson

Nico Patterson

Answered question

2022-11-20

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

Answer & Explanation

erlent00s

erlent00s

Beginner2022-11-21Added 15 answers

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 × 180 o = 540 o
It is known that the sum if the internal angles is 180 o
so the sum of the external angles is: 540 o - 180 o = 360 o

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

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