Answer:
The measure of arc(ADB) is 270 degree.
Step-by-step explanation:
In circle P, it is given that
[tex]\angle APD=128^{\circ}[/tex]
[tex]\angle APB=90^{\circ}[/tex]
We have to find the measure of arc ADB,
[tex]Arc(ADB)=\angle APD+\angle DPC+\angle CPB[/tex] .... (1)
We know that the sum of all central angles of a circle is 360.
[tex]\angle APD+\angle DPC+\angle CPB+\angle APB=360^{\circ}[/tex]
[tex]\angle APD+\angle DPC+\angle CPB+90^{\circ}=360^{\circ}[/tex]
[tex]\angle APD+\angle DPC+\angle CPB=360^{\circ}-90^{\circ}[/tex]
[tex]\angle APD+\angle DPC+\angle CPB=270^{\circ}[/tex] .... (2)
From (1) and (2), we get
[tex]Arc(ADB)=270^{\circ}[/tex]
Therefore the measure of arc(ADB) is 270 degree.
