In the diagram, PR is a diameter, ∠PRQ = (3x-8)° and ∠RPQ = (2y-7)°. Find x in terms of y
A.
\(x=\frac{75-2y}{3}\)
B.
\(x=\frac{105-3y}{2}\)
C.
\(x=\frac{105-2y}{3}\)
D.
\(x=\frac{75-3y}{2}\)
Correct answer is C
180 = ∠RPQ + ∠PRQ + ∠PQR Since PQR = 90 (theorem: angle in a semi circle)
180 = ∠RPQ + ∠PRQ + 90 => 180° = (3x-8)°+(2y-7)°+90°; 90+8+7 = 3x+2y =>\(\frac{105-2y}{3}=x\)