Question

I will give you all my points and mark you the brainliest! Please help

Answer 1

Answer:

$\frac{a}{b}=\frac{5}{3}=>b=\frac{3a}{5}=\frac{270}{5}=54 \\\\x+y=360-(90+54)=360-144=216\\\\\frac{x}{y}=\frac{1}{3}=>y=3x\\ \\x+3x=216\\\\4x=216\\\\x=216:4\\\\x=54\\\\x=b$

Answer 2

Answer and Step-by-step explanation:

Since this is a quadrilateral, we know that all the angles will add up to 360 degrees (by definition). We are given that angle A is 90 degrees and that the ratio of A to B is 5 to 3. This means that we can set up a proportion and solve for B:

A/B = 5/3  ⇒  90/B = 5/3  ⇒  5B = 270  ⇒  B = 54

So, we know that angle B is 54 degrees.

Now that we know angle B is 54 and A is 90, we can find the sum of the remaining two angles X and Y because A + B + X + Y = 360:

90 + 54 + X + Y = 360

X + Y = 216 degrees

We also know that the ratio of X to Y is 1 to 3, so we can set up another proportion:

X/Y = 1/3  ⇒  Y = 3X

Substitute 3X in for Y in X + Y  = 216:

X + 3X = 216

4X = 216

X = 54

Thus, we see that both angles B and X equal 54, so B = X.

Hope this helps!