Question

Angles JHI and GJH are inscribed angles. We have that m∠JHI = One-half b and m∠GJH = One-halfa 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
, One-halfb = m∠JGI + One-halfa. Using the subtraction property, m∠JGI = One-halfb – One-halfa. Therefore, m∠JGI = One-half(b – a) by the distributive property.

Answer 1

Angles JHI and GJH are inscribed angles. We have m∠JHI = 1/2 b and m∠GJH = 1/2 a by the Inscribed Angle Theorem. Angle JHI is an exterior angle of triangle JGI. 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 Exterior Angle Theorem, 1/2 b = m∠JGI + 1/2 a. Using subtraction, m∠JGI = 1/2 b − 1/2 a. Therefore m∠JGI = 1/2(b − a) by the distributive property.