In the diagram, PR is a diameter, ∠PRQ = (3x-8)o and ∠RPQ = (2y-7)o. s x in terms of y
Attached Figure / Diagram
A
\(x=\frac{75-2y}{3}\)
B
\(x=\frac{105-3y}{2}\)
C
\(x=\frac{105-2y}{3}\)
D
\(x=\frac{75-3y}{2}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
180 = ∠RPQ + ∠PRQ + ∠PQR Since PQR = 90 (theorem: angle in a semi circle)
180 = ∠RPQ + ∠PRQ + 90 => 180o = (3x-8)o+(2y-7)o+90o; 90+8+7 = 3x+2y =>\(\frac{105-2y}{3}=x\)
Source: Myschool Past Questions Archive (Record #26679)