Answer:

1. Tridecagon =13 sides

formula for the measure of one interior angle

S= (n-2)180°/n. where n=sides which is n=13

S= (n-2)180°/n

S= (13-2)180°/13

S= (11)180°/13

S= 1980°/13

S=152.30769231 or

S≈152.308° (measure of one interior angle of regular tridecagon)

The sum of exterior angles in a polygon is always equal to 360°. So, we just need to divide 360° to the number of it's side.

S=360°/13

S≈27.69°

2.formula: a=180(s-2)

where a equals the sum of interior angles and s equals the number of sides the polygon has.

a=180(s-2)

a=180(s-2)

4140=180(s-2). divide both side by 180

4140/180=180(s-2)/180

23= (s-2)

23+2= s

25 = s or s = 25

the number of the sides of the polygon is 25

irregular hexagon sum of interior angles: 720°

3.(X+46)+(X+32)+(X+30)+(X+46)+(X+60)+(X+20)= 720°

6X+46+32+30+46+60+20=720°

6X+234°=720°

6X=720°-234°

6X= 486°

6X/6=486°/6

X=81°

X+46

=81+46

=127°

X+32

=81+32

=113°

X+30

=81+30

=111°

X+46

=81+46

=127°

X+60

=81+60

=141°

X+20

=81°+20

=101°

checking

127°+113°+111°+127°+141°+101°=720°

720°=720°

so the answer is correct

Using the fact that interior plus exterior angles at a point add to 180°

4. calculate each exterior

127°+X=180°

X=180°-127°

X= 53°

113°+X=180°

X=180° -113°

X= 67°

111°+X=180°

X=180°-111°

X= 69°

127°+X=180°

X=180°-127°

X= 53°

141°+X=180°

X=180°-141°

X= 39°

101°+X=180°

X=180°-101°

X= 79°

for checking

Sum of the exterior angle of any Polygon is always 360°

53°+67°+69°+53°+39°+79°=360°

360°=360°

so the answer is correct