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.

Step-by-step explanation:

Inscribed Angle Theorem

The inscribed angle theorem states that an angle inscribed in a circle is half of the central angle that subtends the same arc on the circle.

From the given diagram:

Therefore,  by the distributive property.

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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step-by-step explanation:

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