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.

using the information given in the diagram, we can prove that m∠jgi = (b – a), where a and b represent the degree measures of arcs fh and ji.

step-by-step explanation:

1.) angles jhi and gjh are inscribed angles. we have that:

m∠jhi = b and

m∠gjh = a

by the inscribed angle theorem.

2.) 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.

3.) by the substitution property:

b = m∠jgi + a.

4.) using the subtraction property:

b - a = m∠jgi + a - a

b - a = m∠jgi

m∠jgi = b – a

i leave the calculator work to you.

7. diameter 4 miles, circumference 4π miles

8. radius 0.2 miles, circumference 0.4π miles

[this is a bad problem because the actual radius of a car on the track is less than 0.2 miles so the answer is less than 0.4π miles]

9. radius 6 feet, circumference 12π feet

10. diameter 14 cm, circumference 14π cm

11. diameter 4.8 feet, circumference 4.8π feet

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step-by-step explanation: