Point C is on line segment \overline{BD} BD
. Given CD=2x, CD=2x, BD=3x+4,BD=3x+4, and BC=2x-1,BC=2x−1, determine the numerical length of \overline{BD}.
BD
.

the numerical length of segment BD is = 19

Step-by-step explanation:

Given the information that point C is on the segment BD, and understanding that the total segment BD must equal the addition of the two parts on which it is divided by point C, we write the following equation:

BD = BC + CD

now we replace each of the above by their expression in x:

( 3 x + 4 ) = (2 x - 1 ) + (2 x)

and we solve for x in this equation:

3 x + 4 = 2 x + 2 x - 1

3 x +4 = 4 x - 1

4 + 1 = 4 x - 3 x

5 = x

Therefore, we can now obtain the length of segment BD:

BD = 3 x + 4 = 3 (5) + 4 = 15 + 4 = 19

image result for what is another name for consecutive interior angles? ​

when two lines are crossed by another line (called the transversal): the pairs of angles on one side of the transversal but inside the two lines are called consecutive interior angles. in this example, these are consecutive interior angles: d and f.

step-by-step explanation:

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.