Question

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

Answer 1

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°