Question

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.

Answer 1

Answer:

●Inscribed angle theorem

●GJH

●substitution property

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Answer 2

Answer:

• Inscribed Angle Theorem.
• GJH .
• Substitution 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:

• Angles JHI and GJH are inscribed angles.

• We have that $m\angle JHI$ $= \frac{1}{2}b$ and $m\angle GJH$ $= \frac{1}{2}a$ by the Inscribed Angle Theorem. Angle JHI is an exterior angle of triangle GJH .

• Because the measure of an exterior angle is equal to the sum of the measures of the remote interior angles, $m\angle JHI = m\angle JGI + m\angle GJH.$

• By the substitution property, $\frac{1}{2}b$ = $m\angle JGI$ + $\frac{1}{2}a$.

• Using the subtraction property, $m\angle JGI$ = $\frac{1}{2}b-\frac{1}{2}a$.

Therefore, $m\angle JGI$ $=\frac{1}{2}(b-a)$  by the distributive property.