Use the information given in the diagram to prove that m∠JGI = (b – a), where a and b represent the degree measures of arcs FH and JI.

Angles JHI and GJH are inscribed angles. We have that m∠JHI = b and m∠GJH = a by the . Angle JHI is an exterior angle of triangle . Because the measure of an exterior angle is equal to the sum of the measures of the remote interior angles, m∠JHI = m∠JGI + m∠GJH. By the , b = m∠JGI + a. Using the subtraction property, m∠JGI = b – a. Therefore, m∠JGI = (b – a) by the distributive property.