Question

Helppp outt plss....​

Answer 1

Answers:  x = 30 and y = 150

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Explanation:

For any cyclic quadrilateral (aka inscribed quadrilateral), the opposite angles are always supplementary.

One pair of such angles is A and C

A+C = 180

x+y = 180 is one equation to form

The other pair of supplementary angles is B and D

B+D = 180

y-45+2x+15 = 180

2x+y-30 = 180

2x+y = 180+30

2x+y = 210 is the other equation to form

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So the system of equations we have is

$\begin{cases}x+y = 180\\2x+y = 210\end{cases}$

Both equations involve 'y', with the same coefficient, so we can subtract straight down to eliminate this variable.

• The x terms subtract to x-2x = -x
• The y terms subtract to y-y = 0y = 0, so the y terms go away
• The right hand sides subtract to 180-210 = -30

We end up with -x = -30 which solves to x = 30

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Once we know x, we can determine y by plugging it into any equation involving x,y and solving for y

Let's say we picked on the first equation

x+y = 180

30+y = 180

y = 180-30

y = 150

Or we could pick on the second equation

2x+y = 210

2(30) + y = 210

60+y = 210

y = 210-60

y = 150

Only one equation is needed. However, doing both like this shows that we get the same y value, and it helps confirm the answers.