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What is the measure of angle ABC? pls help fast

What is the measure of angle ABC? pls help fast-example-1

1 Answer

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Answer:

(a) 42.5°

Explanation:

You want to know the measure of the external angle at two intersecting secants, when they intercept arcs of 25° and 110°.

External angle

The external angle at B is half the difference of the intercepted arcs:

∠ABC = (110° -25°)/2 = 85°/2

∠ABC = 42.5°

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Additional comment

If the point of intersection (B) moves closer to the circle until it lies on the circle, the secants become chords, and the angle becomes an inscribed angle. Its measure is half the difference between the far arc (AC in this case) and the near arc, which would be zero.

In other words, understanding the relationship in this geometry can help you understand the relationship for inscribed angles.

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