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.

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b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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step-by-step explanation: