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°