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Sergio039 [100]
3 years ago
12

Points A and B are the endpoints of an arc of a circle. Chords are drawn from the two endpoints to a third point, C, on the circ

le.
Given and ,
° and
°.
Mathematics
1 answer:
RSB [31]3 years ago
8 0

Answer:

146°

Step-by-step explanation:

Points A and B are the endpoints of an arc of a circle. Chords are drawn from the two endpoints to a third point, C, on the circle. Given m arch AB=64° and ⦣ABC=73°, m ⦣ABC=__ ° and m arch AC=__ °.

Solution:

Given that:

arc AB = 64° and ⦣ABC=73°

The Central Angle Theorem states that the central angle from two chosen points A and B on the circle is always twice the inscribed angle from those two points. The inscribed angle is any point along the outer arc AB and the two points A and B.

Therefore arc AC is the central angle of ⦣ABC. Using the central angle theorem gives:

arc AC = 2 * ⦣ABC

substituting:

arc AC = 2 * 73

arc AC = 146°

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