Question

What is the value of x?

What is the measure of Angle 1? Angle 1 =
Is Angle 3 complementary to Angle 1? Type "yes" or "no".

Answer 1

x=24; angle1=42; no

Explanation:

angle 3+ angle 4 + angle 5=180

x+18+x+15+4x+3=180

x=24

angle 1 is same as angle 3 (vertical angle)

angle 3=x+18=24+18=42

angle 1+angle 3=42+42≠90, thus not complementary

Answer 2

`\huge\boxed{1. \ x=15}`

`\huge\boxed{2. \ 33 \ \text{degrees}}`

`\huge\boxed{\text{3. No}}`

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.

`x+18+x+15=4x+3`

Now let's solve for x.

`2x+33=4x+3`

`2x+30=4x`

`30=2x`

`x=15`

Now we know the value of x. We can substitute it into the expression for ∠1 (x+18) and find it's value.

`x+18\\15+18\\33`

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.

`33+33=66`

66 is not 90. Therefore these two angles are not complementary.

Hope this helped!