21). what is m∠d? 2). what is the length of side ac of the triangle?

1) The sum of the interior angles of a triangle equals 180°. Let's find ∠AEB first. Add up ∠A + ∠B and subtract your answer from 180°.

14 + 45 = 59
180 - 59 = 121° 

Since ∠AEB and ∠DEC are vertical angles, they must equal the same.
∠DEC = 121°

Now add up ∠DEC and ∠C and subtract your answer from 180 to find ∠D.
121 + 27 = 148
180 - 148 = 32°

m∠D = 32°

2) AB and BC are equal to each because of the Converse of the Base Angle Theorem. Make them equal to each other in an equation.

5x + 5 = 7x - 1
Subtract 5x from both sides.

5 = 2x - 1
Add 1 to both sides.

6 = 2x
Divide both sides by 2.

x = 3

Now plug x in for AC.
6(3) + 7
18 + 7 = 25

AC = 25

The question is kind of confusing. if it's asking how many variations of answers can you give. then do 4^5 for your answer.this would be something like the first question could be a and the 2nd c or first b next c etc. if you can, ask the teacher for a better confirmation of what it's asking. if i'm assuming correctly what it's asking, it's 625 different variations.