Answers: x = 30 and y = 150
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Step-by-step 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
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.