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mojhsa [17]
3 years ago
7

What is the measure of arc BC? 130 65 32.5 180

Mathematics
1 answer:
ale4655 [162]3 years ago
7 0

Answer:

The measure of arc BC is 130° ⇒ 1st answer

Step-by-step explanation:

In a circle:

  • The measure of an arc is equal to the measure of the central angle subtended by it
  • The measure of an arc is equal to double the measure of the inscribed angle subtended by it
  • Central angles subtended by the same arc are equal in measures
  • Inscribed angles subtended by the same arc are equal in measures
  • The measure of central angle is double the measure of the inscribed angle which subtended by its arc

∵ Angle BDC is an inscribed angle

∵ It is subtended by the arc BC

- By using the 2nd fact above

∴ The measure of arc BC = 2 × the measure of ∠BDC

∵ The measure of angle BDC is 65 degree

∴ The measure of arc BC = 2 × 65°

∴ The measure of arc BC = 130°

The measure of arc BC is 130°

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