What is the value of x? What is the measure of angle 6? Show all of your work and/or explain your answer.

1) 5 & 9

5=Corresponding Angle

9=Alternate Exterior Angle

2) 7 & 8

We know 4 is supplementary to 8.  Since that is true, 7 & 8 are also.

8=Corresponing angle to 4

7=Verticle angle to 8

3) We know 1 and 3 equal 180

x-20+x+40=180

2x+20=180

2x=180-20

2x=160

x=80

<2=X+20

=80+20

=100

Angle 2 is the same as angles 5 and 6 added together.

We know angle 5 is the same as angle 1 (corresponding angles).

<1=X-20

=80-20

=60

Now that we know <2=100 and <5=60, we can figure out <6

100-60=40

<6=40°

Step-by-step explanation:

1) 5 & 9

5=Corresponding Angle

9=Alternate Exterior Angle

2) 7 & 8

We know 4 is supplementary to 8.  Since that is true, 7 & 8 are also.

8=Corresponing angle to 4

7=Verticle angle to 8

3) We know 1 and 3 equal 180

x-20+x+40=180

2x+20=180

2x=180-20

2x=160

x=80

<2=X+20

=80+20

=100

Angle 2 is the same as angles 5 and 6 added together.

We know angle 5 is the same as angle 1 (corresponding angles).

<1=X-20

=80-20

=60

Now that we know <2=100 and <5=60, we can figure out <6

100-60=40

<6=40°

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.