Use the given information to find the measures of all angles formed by parallel lines a and b, and transversal m. b One angle is 25° greater than another. Correct answer gets brainliest!

∠1 = ∠3 = ∠5 = ∠7 = 77.5°

∠2 = ∠4 = ∠6 = ∠8 = 102.5°

Step-by-step explanation:

In the picture attached, the parallel lines and the transversal are shown.

8 angles are formed, where:

∠1 ≅ ∠3 ≅ ∠5 ≅ ∠7

∠2 ≅ ∠4 ≅ ∠6 ≅ ∠8

On the other hand, ∠1 + ∠2 = 180°, and ∠2 is 25° greater than ∠1, that is ∠1 + 25° = ∠2, therefore:

∠1 + ∠1 + 25° = 180°

2∠1 = 180° - 25°

∠1 = 155°/2

∠1 = 77.5°

and

∠2 = 77.5° + 25° = 102.5°

<1=<5

<4=<8

<2=<6

<3=<7[these all are corresponding angle]

<1=<3

<4=<2

<8=<6

<5=<7 [these all are vertically opposite angle]

let<1=70°

than

<1=<5=<7=<3=77°

again

<1+<2=180°[linear pair]

<2=180°-72=98°

Than

<2=<6=<4=<8=98°

b One angle is 25° greater than another.

let <1=x than <2=<x+25°

<1+<2=180°[linear pair]

x+x+25=180°

2x=180-25

x=155.2

x=77.5°

x+25=77.5°+25°=102.5°

either

<1=<5=<7=<3=77°

<2=<6=<4=<8=102.5°

Or

<1=<5=<7=<3=102.5°

<1=<5=<7=<3=102.5°<2=<6=<4=<8=77°

it is a. 4.2 because 7.6-3.4 gets the remaining length of 4.2. i might be wrong but i am pretty sure this is the answer.

δabc ≅ δdcb by sas because

db ≅ ac . . given (side)

bc ≅ bc . . reflexive property (side)

∠dbc ≅ ∠ acb . . alternate interior angles where transversal bc crosses parallel lines bd and ac (included angle)