Pic attached
the following flowchart with missing statements and reasons proves that the measure of angle ecb is 43°:
which statement and reason can be used to fill in the numbered back spaces?
a) 1. corresponding angles are congruent
2. triangle sum theorem
3. measure of angle aed is 43°
b) 1. alternate interior angles are congruent
2. base angle theorem
3. measure of angle aed is 47°
c) 1. base angle theorem
2. corresponding angles are congruent
3. measure of angle aed is 43°
d) 1. alternate interior angles are congruent
2. triangle sum theorem
3.measure of angle aed is 47°

i believe

step-by-step explanation:

from my conclusion c

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15