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

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°

astha8579 astha8579 · Answer 2 · 2022-01-22T09:46:05+01:00

Using the property that angle subtended by an arc on center is double than on circumference, you can find measure of arc BC.

The angle subtended by arc BC on center of circle is of 2 times 65 = [tex]130^\circ[/tex]

Thus, option A: 130 is correct

Length of arc BC

"Angle subtended by an arc of a circle on its center is double than angle subtended by it on circumference"

Thus, angle subtended by arc BC on center of circle is of 2 times 65 = [tex]130^\circ[/tex]

Thus, option A: 130 is correct

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