How do you solve these questions? I am very confused

1. a, b, and c all equal 54

2. d and b are 65, c and a are 115

3. b is 126, idk about a

4. yes they are parallel

5. no they are not parallel

6. yes they are parallel

7. b= 78, a= 102, c= 64, d= 116, e= 26, f= 58

8. x = 80

9.  x= 20 and  y= 25

Step-by-step explanation:

1. <a is vertical to the given angle so they are both the same measure (54)

<c corresponds to <a so they have the same measure

<b corresponds to <54 so they have the same measure

(note: when angles correspond in parallel lines with a transversal, this means that one angle on a line is located in the same as another angle on the parallel line)

2. <65 corresponds to <d so they are the same measure

<d and <b would be considered vertical angles since b corresponds to the angle opposite to d, so they are the same measure

<d and <c are supplementary, so they add up to 180. We know that d is 65 so subtract 65 from 180 to get 115. <c is 180

<c and <a correspond so they have the same measure

3. <54 and <b are supplementary so they equal to 180. subtract 54 from 180 to get 126. <b is 126

4. <62 corresponds to the angle the supplements <118. add 118 and 62 and you get 180. if you do the same process on the line below the first line, you will get the same angles that equal to 180 (62 and 118)

this means that the lines are parallel because the corresponding angles have equal measures

5. if the lines were parallel, then <95 and <25 should be supplementary and add up to 180. But when you do add them, they equal 120, this means that the lines are not parallel.

6. <48 and <48 are corresponding angles

7. <b is 78 because it is corresponding to the given <78

<a is 102 because it corresponds to the angle supplementary to <78, and the measure of the supplementary angle is 102

<c is 64 because it corresponds to the angle vertical to the given <64, so they are the same measure

<d is 116 because it is supplementary to <c and the measure of the supplementary angle would be 116

<e is 26 because <e+90 is corresponding to <d, so set the equation to e + 90 = 116. You will get that <e is 26

<f is 58 because  f+78+?= 180. We know that ? is 44 because the angles are vertical angles, so now the equation would be f + 78 + 44 = 180. Solve this to get <f is 57

8. <x corresponds to the angle vertical to <3x- 160

set the equation as x = 3x - 160 and solve it to get x = 80

9. <182-4x is vertical to <5x+2

set the equation to 182 - 4x = 5x + 2  and solve to get x = 20

since every angle shown is congruent, plug in the value of x to an equation to find every angle measure

every given angle measure is 102

so to find y, you can say 4y + 2 = 102

solve to get y = 25

step-by-step explanation:

i only know the sequence of arithmetic it adds the first is 5+4 then it goes up as it adds to then it is 9+5 then 14+6 then to 20+7 and so on. 5,9,14,20,27,35.

step-by-step explanation: