Help me do this problem plz

m<A = 84

Step-by-step explanation:

1. Approach

Using the same-side interior angles are supplementary angles theorem, one can form an equation and solve for the unknown value (x). Then one can substitute the answer back into the expression that is given, and solve for the m<A.

2. Solve for (x)

When two parallel lines are intersected by a transversal line, then the same-side interior angles are supplementary, meaning that their angle measures add up to 180 degrees. Using this information, one can form an equation and solve for the value of (x).

m<A + m<B = 180

( 5x + 34 ) + ( 2x + 76 ) = 180

Simplify; combine like terms,

7x + 110 = 180

Inverse operations,

7x + 110 = 180

     -110    -110

7x = 70

/7    /7

x = 10

3. Solve for m<A

Now that one has the value for the parameter (x), one can substitute this into the equation that has been given for (m<A), and solve for the value of (m<A).

m<A = 5x + 34

5(10) + 34

50 + 34

84

let's add {f(x)=x+1}f(x)=x+1 and {g(x)=2x}g(x)=2x together to make a new function.

f(x)+g(x) =(x+1)+(2x)=x+1+2x=3x+1

let's call this new function hh. so we have:

{h(x)}={f(x)}+{g(x)}{=3x+1}h(x)=f(x)+g(x)=3x+1

we can also evaluate combined functions for particular inputs. let's evaluate function hh above for x=2x=2. below are two ways of doing this.

method 1: substitute x=2x=2 into the combined function hh.

h(x)

h(2)

​    

=3x+1

=3(2)+1

=7

​ since h(x)=f(x)+g(x)h(x)=f(x)+g(x), we can also find h(2)h(2) by finding f(2) +g(2)f(2)+g(2).

first, let's find f(2)f(2):

f(x)

f(2)

​    

=x+1

=2+1

=3

​  

now, let's find g(2)g(2):

g(x)

g(2)

​    

=2x

=2⋅2

=4

​  

so f(2)+g(2)=3+4=\greend7f(2)+g(2)=3+4=7.

notice that substituting x =2x=2 directly into function hh and finding f(2) + g(2)f(2)+g(2) gave us the same answer!