WILL GIVE BRAINLIEST IF FULL COMPLETE CORRECT ANSWER IS GIVEN. Sarah has some large, polygon-shaped cardboard cutouts that she needs to sort, because she wants to hang them in her geometry classroom. The first division she needs to make is to divide the regular polygons from the irregular ones. In order to save time measuring all angles and sides of each polygon, and owing to the size and number of sides/angles in each shape, Sarah decides to measure just one angle in each polygon. Consider the following angle measures for polygons A through T, and answer the following questions.
a. If each angle measure represented an exterior measure of its polygon, which of the polygons could be regular? Explain your answers.

b. If each angle measure represented an exterior measure of a regular polygon, name each polygon by using its number of sides. (For any figure with more than 12 sides, just use the number: e. g. 45-gon.)

c. If each angle measure represented an interior measure of its polygon, which of the polygons could be regular? Explain your answers.

d. If each angle measure represented an interior measure of its polygon, which of the polygons do we know are convex? Explain your answers.

  a. ABCDEFHILO

  b. 36- 24- 18- dodeca- nona- octa- hexa- penta- square, triangle

  c. HLNOPQ

  d. ABCD EFGH IJKL MNOP Q

Step-by-step explanation:

a. The exterior angles of a regular polygon have a measure that is 360° divided by the number of sides. If the angle has an integer value, that value must be a divisor of 360°.

Possible regular polygons are ...

  ABCDEFHILO

__

b. A: 36-gon; B: 24-gon; C: 18-gon; D: dodecagon; E: nonagon; F: octagon; H: hexagon; I: pentagon; L: square; O: triangle

__

c. The supplement of a regular polygon's interior angle is equal to 360° divided by the number of sides. That is, the angle's supplement must be a divisor of 360°.

Possible regular polygons are ...

  HLNOPQ

__

d. In order for a polygon to be convex, it can have no reflex interior angles. That is, all interior angles must be at most 180°. Only polygons R, S, T cannot be convex.

Possible convex polygons are ...

  ABCD EFGH IJKL MNOP Q

for this case we have by definition, if two lines are perpendicular, then the product of their slopes is -1.

then, given the following line:

so,

we are looking for m_ {2}:

then, the line is given by:

we find "b" replacing the given point:

finally, the equation is:

option c

x =-.20752

step-by-step explanation:

4^(x+2)=12

4^(x+2)=12

take the log base 4 on each side

log 4 (4^(x+2) = log 4(12)

we know log b(a^y) = y log b (a)

(x+2) log 4(4) = log 4 (12)

x+2 = log 4 (12)

we know   logb c = loga c/loga b

we want to convert to base 10   so a = 10

by default, we do not write the 10   c = 4   and b = 10

log4 10 = log 12/log 4

log4 10 = log 12/ log 4

x+2 = log 12/ log 4

subtract 2 from each side

x +2 -2 = log 12/ log 4 -2

x = 1.79248125 -2

x =-.20752