Answer: The measure of ∠ABC = 54°.
Step-by-step explanation:
As we know that
Measure of major arc AC = 234° ( Far arc)
Measure of minor arc AC = 126° (Near arc)
By theorem, we know that the angle formed by intersection of two tangents is equal to half the difference of far arc and near arc.
As we know that ∠ABC is given by
[tex]\frac{1}{2}(Far\ arc-Near\ arc)\\\\=\frac{1}{2}(234-126)\\\\=\frac{1}{2}\times 108^\circ\\\\=54^\circ[/tex]
Hence, the measure of ∠ABC = 54°.
Answer:
54 degrees
Step-by-step explanation:
Given is a circle O.
The centre is O.
Angle AOC = 126
AB and BC are tangents to the circle
COnsider the quadrilatral ABCO.
Since AB and BC are tangents they both are perpendicular to their corresponding radius.
IN quadrilateral ABCO,we have two angles 90 degrees and one angle AOC=126
Since sum of angles = 180
we have angle ABC = 360-(90+90+126)=54 degrees
