Question

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

Answer 1

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°