Question

WILL GIVE BRAINLIEST ANSWER TO THE FIRST PERSON TO ANSWER CORRECTLY!

Answer 1

Answer with explanation:

A Polygon is said to be convex, if all the diagonals of the polygon lies in the interior of the polygon.

→Sum of interior angle of polygon =(n-2)×180°, where n is the number of sides of the polygon.-----(1)

→A pentagon is said to be convex, if it has 5 sides and all the Diagonals of pentagon lies in the interior.

Sum of interior Angles of Triangle =(3-2)×180°=180°

Sum of interior angles of Quadrilateral = (4-2)×180°=2×180°=360°

Sum of Interior angles of Polygon =(5-2)×180°=3×180°=540°

Used the formula (1) in all the three cases.

Answer 2

In a convex polygon, all interior angles are less than or equal to 180. So pentagons are polygons of five sides. We need to draw two different pentagons with the previous characteristics and measures of the internal angles. Therefore, we will choose to type of pentagons.

Every pentagon can be divided up into three triangles, either a regular or irregular one and each triangle adds up to 180 degrees. Therefore, the angles in every pentagon must add up to 540 degrees.

1. Drawing of the first convex pentagon (Regular Pentagon).

A polygon is regular when all angles are equal and all sides are equal. The regular pentagon is a 5-sided polygon. This is shown in Figure 1. Note that all angles are equal to 108°.

1.1. Sum of the interior angles of the first convex pentagon.

According to Figure 1, the sum of its interior angles is as follows:

$\alpha=5 \times 108^{\circ}=540^{\circ}$

As we said, the angles in every pentagon must add up to 540 degrees. If the pentagon is regular each internal angle measures 108°. In fact, in a Regular Polygon with N sides, each angle is:

$\frac{(N-2)180{^\circ}}{N} \\ \\ Since \ N=5 \\ \\ \\ \frac{(5-2)180{^\circ}}{5}= 108^{\circ}$

2. Drawing of the second convex pentagon (Irregular Pentagon)

This is a type of polygon that does not have all sides equal and all angles equal. In Figure 2 is shown this pentagon. Note that there are five sides and all angles are not equal.

2.1 Sum of the interior angles of the second convex pentagon.

According to Figure 2, the sum of its interior angles is given by:

 $\beta=81^{\circ}+139^{\circ}+139^{\circ}+94^{\circ}+87^{\circ}=540^{\circ}$

As we said, no matter if the pentagon is irregular, the angles in every pentagon must add up to 540 degrees.