Given:
Given that the measure of ∠CDR = 85°
We need to determine the measure of [tex]\widehat{RC}[/tex] and [tex]\widehat{CBR}[/tex]
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;
[tex]m\angle CDR = m \widehat{RC}[/tex]
Substituting the values, we get;
[tex]85^{\circ} = m \widehat{RC}[/tex]
Thus, the measure of [tex]\widehat{RC}[/tex] 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;
[tex]m\widehat{CBR}=360^{\circ}-m \widehat{RC}[/tex]
Substituting the values, we have;
[tex]m\widehat{CBR}=360^{\circ}-85^{\circ}[/tex]
[tex]m\widehat{CBR}=275^{\circ}[/tex]
Thus, the measure of [tex]\widehat{CBR}[/tex] is 275°
