A convex figure with three sides is triangle. The sum of the measures of all interior angles of the triangle is 180°.
Let [tex]\alpha, \beta, \gamma[/tex] be interior angles of this triangle. Then
[tex]\alpha+\beta+\gamma=180^{\circ}.[/tex]
Find exterior angles of this triangle:
1. [tex]180^{\circ}-\alpha[/tex] is exterior angle adjacent to the interior angle [tex]\alpha.[/tex]
2. [tex]180^{\circ}-\beta[/tex] is exterior angle adjacent to the interior angle [tex]\beta.[/tex]
3. [tex]180^{\circ}-\gamma[/tex] is exterior angle adjacent to the interior angle [tex]\gamma.[/tex]
The sum of the measures of all exterior angles is
[tex]180^{\circ}-\alpha+180^{\circ}-\beta+180^{\circ}-\gamma=540^{\circ}-(\alpha+\beta+\gamma)=540^{\circ}-180^{\circ}=360^{\circ}.[/tex]
Answer: 360°
