Given: circle k(O) m∠R = (12x+1) m FP = (11x+7) m PQ = 60 Find: m FP

Question

   

    

Answer 1

Angle R is an inscribed angle that equals half its intercepted arc (arc FQ). Arc FQ is equal to the sum of arc FP + arc PQ.

That leads to the equation 12x+1 = 1/2(11x+7 + 60). Multiplying both sides by 2 leads to:

24x+2 = 11x+67.

Solve for x and substitute that value into the expression for the measure of arc FP.