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The circle shown below has AB and BC as its tangents.



If the measure of arc AC is 120°, what is the measure of angle ABC?

60°

70°

40°

65°

The circle shown below has AB and BC as its tangents If the measure of arc AC is 120 what is the measure of angle ABC 60 70 40 65 class=

Respuesta :

SJ2006

It would be:  180-120 = 60

'cause internal & external make 180 degree of angle in total.

SO, OPTION A IS YOUR ANSWER

boffeemadrid

Answer:

(A)

Step-by-step explanation:

We know that The measure of the external angle is the semi difference of the arcs that it covers.

so, the arcs that it covers are arc AC and arc ABC.

Thus, We have

AB and BC as its tangents, the measure of arc AC is 120°, therefore according to the theorem on circles,

360°=arc AC + arc ABC

360°=120°+arc ABC

arc ABC=240°

Then, ∠ABC=[tex]\frac{1}{2}{\times}(240-120)[/tex]

=[tex]\frac{1}{2}{\times}120=60^{{\circ}}[/tex]

Therefore, the measure of angle ABC=60°.

Hence, option a is correct.

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