The second degree polynomial with leading coefficient of -2 and root 4 with multiplicity of 2 is:

<h3>
How to write the polynomial?</h3>
A polynomial of degree N, with the N roots {x₁, ..., xₙ} and a leading coefficient a is written as:

Here we know that the degree is 2, the only root is 4 (with a multiplicity of 2, this is equivalent to say that we have two roots at x = 4) and a leading coefficient equal to -2.
Then this polynomial is equal to:

If you want to learn more about polynomials:
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Notice the point R
is a vertex between two "vertical angles"

those two folks are also the same
so now, we have the left triangle has angle P equals to angle T on the other triangle
we also have the side on the left triangle of PR equals the side of TR on the other triangle, and those two verticals angles are equal to each other
does ASA ring a bell?
Call x and y those angles. If they are complementary, then their sum equals 90°:
x + y = 90°
y = 90° - x
The ratio of them is 5 to 1. So,
x/y = 5/1
x/(90° - x) = 5/1
x = 5 * (90° - x)
x = 450° - 5x
x + 5x = 450°
6x = 450°
x = 450°/6
x = 75°
The measure of the other angle is
y = 90° - 75°
y = 15°
The angles are 75° and 15°.
I hope it helps. =)