Question

Using the image, determine the length of each arc.
m RC=
m CBR =

Answer 1

Given:

Given that the measure of ∠CDR = 85°

We need to determine the measure of
`\widehat{RC}` and
`\widehat{CBR}`

Measure of arc RC:

Since, we know that if a central angle is formed by two radii of the circle then the central angle is equal to the intercepted arc.

Thus, we have;

`m\angle CDR = m \widehat{RC}`

Substituting the values, we get;

`85^(\circ) = m \widehat{RC}`

Thus, the measure of
`\widehat{RC}` is 85°

Measure of arc CBR:

We know that 360° forms a full circle and to determine the measure of arc CBR, let us subtract the values 360 and 85.

Thus, we have;

`m\widehat{CBR}=360^(\circ)-m \widehat{RC}`

Substituting the values, we have;

`m\widehat{CBR}=360^(\circ)-85^(\circ)`

`m\widehat{CBR}=275^(\circ)`

Thus, the measure of
`\widehat{CBR}` is 275°