Use the figure below and determine the angle measures. what is the measure of angle G?

45

Step-by-step explanation:

First we want to understand the Base Angles Theorem

The Base Angles Theorem tells us that the base angles or the two bottom angles of an isosceles triangle are congruent.

Using this theorem, we can say that angle A and angle G are congruent meaning m∠A = m∠G. We can then write both of them as x.

We can create the equation ∠N + ∠A + ∠G = 180 degrees.

Knowing ∠N and knowing ∠A + ∠G = 2x, we can rewrite the equation into

90 + 2x = 180

We can then solve for x,

90 + 2x - 90 = 180 - 90

2x = 90

2x / 2 = 90 / 2

x = 45 degrees

468

step-by-step explanation:

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!