Start overline, A, C, end overline are diameters of circle
P
PP.

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°.

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