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In cyclic quadrilateral PQRS,

Find the largest angle in quadrilateral PQRS, in degrees.

 Aug 26, 2023

Best Answer 

 #3
avatar+128398 
+1

P  and R  are  opposite angles in the quadrilateral  such that

 

P  = (3/5)R           so R > P

 

So

 

P  + R  = 180

 

(3/5)R + R  = 180

 

(8/5)R = 180

 

R = 180 * 5/8  =   112.5°

 

And Q =  (4/5)R = (4/5) (112.5)  =   90°

 

So  S  must also   = 90°   since Q and S are supplemental

 

So  R  is the largest angle

 

 

cool cool cool

 Aug 27, 2023
 #1
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0

 

Let P=3x,Q=4x,R=5x. Then, the sum of the angles in quadrilateral PQRS is [3x + 4x + 5x + 6x = 180^\circ,]so x=30∘. The largest angle is ∠R=5⋅30∘=150∘​.

 Aug 26, 2023
 #2
avatar+14 
0

im not sure if the math there adds up because then (3x+4x+5x+6x) = 180 would make x equal to 10

samsungtawe  Aug 27, 2023
 #3
avatar+128398 
+1
Best Answer

P  and R  are  opposite angles in the quadrilateral  such that

 

P  = (3/5)R           so R > P

 

So

 

P  + R  = 180

 

(3/5)R + R  = 180

 

(8/5)R = 180

 

R = 180 * 5/8  =   112.5°

 

And Q =  (4/5)R = (4/5) (112.5)  =   90°

 

So  S  must also   = 90°   since Q and S are supplemental

 

So  R  is the largest angle

 

 

cool cool cool

CPhill Aug 27, 2023

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