Question

Need help!!!
In the diagram of circle o, what is the measure of ABC?
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Answer 1

54 degrees

Explanation:

I would turn this into a quadrilateral by connecting C to O and O to A.

The angles of a quadrilateral add up to 360 degrees.

So we have 90+90+126+angleABC=360

180+126+angleABC=360

306+angleABC=360

angleABC=360-306=54

Answer 2

ABC = 54°

Explanation:

Two tangent have been drawn from an external point B to the circle O.

These tangents touch the circle at points A and C.

Now as per Theorem of arcs and angles.

∠ABC =
`(1)/(2)` [m(major arc AC) - m(minor arc AC)]

=
`(1)/(2)` [234 - 126]

=
`(1)/(2)` × (108)

= 54°

Therefore, ABC = 54°