Given:
m∠APB = 19°
To find:
The arc measure of DBC.
Solution:
∠APB and ∠DPC are vertical angles.
By vertical angle theorem:
m∠APB = m∠DPC
m∠DPC = 19°
DB is the diameter of the circle.
Angle measure of diameter = 180°
m∠DPB = 180°
m∠DPC + m∠CPB = m∠DPB
19° + m∠CPB = 180°
Subtract 19° from both sides.
19° + m∠CPB - 19° = 180° - 19°
m∠CPB = 161°
The measure of central angle is equal to the measure of intercepted arc.
m∠CPB = m(ar CPB)
m(ar CPB) = 161°
The arc measure of DBC is 161°.
