Question

The given shape is a regular pentagon.

Answer 1

Answer:

Step-by-step explanation:

Since there are missing data, let's discuss some facts about regular polygons and their angles.

1) The sum of its Interior angles is given by:

$S_i=180^{\circ}(n-2) \therefore \:for\: a\:pentagon\:S_i=180^{\circ}(5-2) =540^{\circ}$

2) Since it is a regular pentagon, each interior angle is congruent:

Each interior angle:

$Interior\:angle=\frac{540^{\circ}}{5} =108^{\circ}$

3) If we trace an outside line, the external angle will be supplemental, i.e.

$m\angle external= 180^{\circ}-108^{\circ} \therefore= 72^{\circ}$

4) If we trace from each diagonal one line segment, in a regular pentagon that will form 3 triangles with one-third of 108º,i.e.,36º

As we can see, the in the picture below