The circle shown below has AB and BC as its tangents: AB and BC are two tangents to a circle which intersect outside the circle at a point B. If the measure of arc AC is 130°, what is the measure of angle ABC? (1 point) 55° 50° 60° 65°
2 answers:
We are given with arc AC = 130 The measure of the arc on the other side of the circle is 360 - 130 = 230 Therefore, according to the theorem on circles, the measure of angle ABC is (1/2) ( 230 - 130) = 50
he picture in the attached figure
we know that
The measure of the external angle is the semidifference of the arcs that it covers.
so
the arcs that it covers are
arc AC and arc ABC
We have
AB and BC as its tangents
the measure of arc AC is °
In addition, a circle has degrees by definition
so
°= arc AC + arc ABC
°= ° + arc ABC
arc ABC= °- °= °
Then
Angle ABC =
Angle ABC= °
therefore
the answer is
Angle ABC= °
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