What is the measure of ABC?

Mathematics

1 answer:

Viefleur [7K]3 years ago

5 0

Answer:

Step-by-step explanation:

Hi there!

In order to find the answer to this question we must know about:

The angles of intersecting chords theorem

The theorem states that if two chords intersect the angles formed at the intersection is equal to half the sum of its intercepted arc and it's vertical angle's intercepted arc.

Angle ABC is formed by intersecting chords meaning that the measure of angle ABC is equal to half the sum of its intercepted arc + it's vertical angle's intercepted arc ( angle ABC vertical angle is angle EBD. Angle EBD's intercepting arc is arc ED. )

Angle ABC intercepted arc is AC

Hence Angle ABC = 1/2 ( arc AC + arc ED)

Arc ED = 44 and arc AC = 82

Thus, angle ABC = 1/2(82 + 44)

82 + 44 = 126

126/2=63

Hence Angle ABC = 63

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