A convex figure has three sides what is the sum of its exterior angles

Question

asked Oct 12, 2019 152k views

1 Answer

RenatoSz · Answer 1 · 2019-10-16T14:13:12+0000

A convex figure with three sides is triangle. The sum of the measures of all interior angles of the triangle is 180°.

Let
$\alpha, \beta, \gamma$ be interior angles of this triangle. Then

$\alpha+\beta+\gamma=180^(\circ).$

Find exterior angles of this triangle:

1.
$180^(\circ)-\alpha$ is exterior angle adjacent to the interior angle
$\alpha.$

2.
$180^(\circ)-\beta$ is exterior angle adjacent to the interior angle
$\beta.$

3.
$180^(\circ)-\gamma$ is exterior angle adjacent to the interior angle
$\gamma.$

The sum of the measures of all exterior angles is

$180^(\circ)-\alpha+180^(\circ)-\beta+180^(\circ)-\gamma=540^(\circ)-(\alpha+\beta+\gamma)=540^(\circ)-180^(\circ)=360^(\circ).$

Answer: 360°