Derek wrote the following paragraph proof for the vertical angles theorem:

the sum of angle 1 and angle 4 and the sum of angle 3 and angle 4 are each equal to 180 degrees by the definition of supplementary angles. the sum of angle 1 and angle 4 is equal to the sum of angle 3 and angle 4 by the transitive property of equality. angle 1 is equal to angle 3

which phrase completes the proof?

a. by construction using a straightedge
b. by the definition of a perpendicular bisector
c. by the subtraction property of equality
d. by the vertical angles theroem

Option C is correct.

By the Subtraction Property of Equality.

Explanation:

Supplementary Angles: Two angles are Supplementary if the sum of the  measure of angles is 180 degree.

Given:

   {By definition of supplementary angle}                                              .......[1]

Transitive Property of equality:

If a=b and

b = c,

then a = c

By the transitive property,

[1} ⇒            ......[2]

Subtraction property of equality states that you subtract the same number from both sides of an equation.

Subtract from both the sides in [2];

Simplify:

    {By subtraction property of equality}

Therefore, the only phrase which completes the proof is; by the subtraction property of equality

see below

step-by-step explanation:

7.   there are 10 data points in the set.   the middle point is between 5 and 6.   the middle point in the top half is 8   and the middle point in the bottom half is 3. to find the iqr , take point 8 and subtract point 3

mid term   point 8 = 100   point 3 = 88

iqr = 100-88 = 12

final   point 8 = 93   point 3 = 78

iqr = 93 - 78 = 15

the final has the greatest iqr

6.   b - there is a high data value that causes the data set to be asymmetrical for the males: the data for males are high and asymmetrical .   there is an outlier for the males that skews the data

5.   the   iqr is a better measure of spread for the movies and basketball games.   since the basketball game has an outlier, we do not want to use standard deviation for measurement.  

3.   the exam median is much higher than the class median.   the median line is farther to the right on the exams

2.   there is no way to tell what the means are from the box and whisker plots.