Answer:
[tex]\huge\boxed{1. \ x=15}[/tex]
[tex]\huge\boxed{2. \ 33 \ \text{degrees}}[/tex]
[tex]\huge\boxed{\text{3. No}}[/tex]
Step-by-step explanation:
To solve for x, what we need to note is that this is a line intersecting 4 nearly 90° angles.
All of those angles are the same.
We can see that angles ∠3, ∠4 and ∠1 are formed with this intersection line.
This means that ∠3 and ∠4 added together will be ∠5.
Since we know ∠3, ∠4, and ∠5 we can solve for x by creating an equation.
[tex]x+18+x+15=4x+3[/tex]
Now let's solve for x.
[tex]2x+33=4x+3[/tex]
[tex]2x+30=4x[/tex]
[tex]30=2x[/tex]
[tex]x=15[/tex]
Now we know the value of x. We can substitute it into the expression for ∠1 (x+18) and find it's value.
[tex]x+18\\15+18\\33[/tex]
So ∠1 is 33 degrees.
Complementary angles are two that, when added to each other, are 90 degrees. Since we know that ∠1 and ∠3 are opposite angles, we know their angle measurements must be the same. This means both ∠1 and ∠3 are 33 degrees.
HOWEVER, in order for them to be complementary, both angles added together must be 90.
[tex]33+33=66[/tex]
66 is not 90. Therefore these two angles are not complementary.
Hope this helped!
