1. The number of sides of the polygon is of: 12 sides.
2. The missing exterior angles are of: α = 48.5º.
3. The size of the exterior angle is of 20º, hence the polygon has 18 sides.
<h3>What is the relation between the measure of the exterior angles and the number of sides of a regular polygon?</h3>
A regular polygon is a polygon in which all the sides have the same length.
The relation between the measure of the exterior angles of a regular polygon and the number of sides is given as follows:
Measure of each angle = 360º/number of sides.
For item a, the measure of each angle is of 24º, hence the number of sides is obtained as follows:
24º = 360º/number of sides.
24n = 360
n = 360/24
n = 12 sides.
The sum of the measures of the external angles of a polygon is always of 360º.
Hence, for item 2, the missing angles are obtained as follows:
2α + 90 + 55 + 40 + 78 = 360
2α + 263 = 360
2α = 97
α = 97/2
α = 48.5º.
An interior angle and it's exterior angle are supplementary, hence, for item 13, the measure of the exterior angle is of:
Exterior angle = 180º - 160º = 20º.
Then the number of sides of the polygon is obtained as follows:
20n = 360
n = 360/20
n = 18 sides.
A similar problem, also featuring polygons, is presented at brainly.com/question/224658
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