Question

A circle with circumference \blue{8}8start color #6495ed, 8, end color #6495ed has an arc with a 288^\circ288

∘

288, degrees central angle.

What is the length of the arc?

Answer 1

122°

The measure of the central angle is twice the measure of the inscribed angle that subtends the same arc.

∠ABC = 2×∠ADC = 2×61°

∠ABC = 122°

Step-by-step explanation:

Answer 2

The arc is 6.4 units long.

Step-by-step explanation:

For a circle of radius R, the circumference is given by:

C = 2*pi*R

If we have a section of this circle defined by an angle θ (such that this section makes an arc), the length of that arc is:

A = (θ/360°)*2*pi*R

and 2*pi*R is the circumference, then we can write the length of the arc as:

A = (θ/360°)*C

qsIn this case, we know that the circumference is equal to 8 units, and the arc has an angle of 288°

Then the length of that arc is:

A = (288°/360°)*C = (288°/360°)*8 = 6.4

The arc is 6.4 units long.