Question

Lines b and c are parallel. What is the measure of 2? m2 = 31° m2 = 50° m2 = 120° m2 = 130°

Answer 1

2.
`m\angle 2=50^(o)`

Step-by-step explanation:

We have been given that lines b and c are parallel.

Since we know that vertical angles are always congruent. We can see that measure of angle 2 will be equal to
`(7x+1)^(o)` as it is the measure of vertical angle of angle 2.

We can see that
`(7x+1)^(o)` and
`(18x+4)^(o)` form a linear pair, so they will add up to 180 degrees.

`18x+4+7x+1 =180`

`25x+5=180`

`25x=180-5`

`25x=175`

`x=(175)/(25)`

`x=7`

Now let us substitute value of x in the expression
`(7x+1)^(o)` to find the measure of angle 2.

`m\angle 2=7x+1`

`m\angle 2=7* 7+1`

`m\angle 2=49+1`

`m\angle 2=50`

Therefore, the measure of angle 2 will be 50 degrees and 2nd option is the correct choice.

Answer 2

m2 = 50

Explanation:

7x+1+18x+4=180

25x+5=180

25x=175

x=7

m2= 7(7)+1 = 50