Mathematics: What is the measure of EAB in circle F? 72° 92° 148° 200°

C. Alternate interior anglesStep-by-step explanation:they re on the inside but of opposite sides of line RK...

What is the measure of EAB in circle F? 72° 92°

Phalanndwachris8740

26.01.2022

We have been given a diagram. We are asked find the measure of arc EAB.

First of all, we will find the measure of arcs ED and CB using our given information.

We know that measure of an inscribed angle is half the measure of intercepted arc.

We can see that angle EBC is inscribed angle of arc EDC, so measure of arc EDC will be twice the measure of angle EBC.

$\widehat{EDC}=2\times m\angle EBC$

$\widehat{EDC}=2\times 80^{\circ}$

$\widehat{EDC}=160^{\circ}$

Similarly, we will find the measure of arc DCB.

$\widehat{DCB}=2\times m\angle DEB$

$\widehat{DCB}=2\times 70^{\circ}$

$\widehat{DCB}=140^{\circ}$

$\widehat{ED}=\widehat{EDC}-\wdiehat{DC}$

$\widehat{ED}=160^{\circ}-88^{\circ}$

$\widehat{ED}=72^{\circ}$

$\widehat{ED}+\widehat{DCB}+\widehat{EAB}=360^{\circ}$

$72^{\circ}+140^{\circ}+\widehat{EAB}=360^{\circ}$

$212^{\circ}+\widehat{EAB}=360^{\circ}$

$\widehat{EAB}=360^{\circ}-212^{\circ}$

$\widehat{EAB}=148^{\circ}$

Therefore, the measure of arc EAB is 148 degrees and option C is the correct choice.

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