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An cyclic quadrilateral VWXY is inscribed in circle Z. If ∠𝑋=2𝑥−50 and ∠𝑉=3𝑥+20, what is the value of x?

 
 Jun 3, 2021
edited by Guest  Jun 3, 2021
 #1
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The special properties a cyclic quadrilateral has is that 

 

1. All 4 vertices lie on the edge of some circle. 

2. Opposite angles add up to $180°$ 

 

Thus, applying #2 here gives us $2x-50 + 3x+20 = 180 \rightarrow \boxed{x = 42}$, which is our answer. 

 
 Jun 3, 2021

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