Given:
The figure of a circle.
To find:
The measure of arc AD and measure of each arc.
Solution:
The measure of arc is equal to the central angle of that arc.
The central angle of arc AD is 105 degrees. So,
[tex]m(arc(AD))=105^\circ[/tex]
The central angle of arc BC is 35 degrees. So,
[tex]m(arc(BC))=35^\circ[/tex]
The central angle of arc CD is 50 degrees. So,
[tex]m(arc(CD))=50^\circ[/tex]
The central angle of a complete circle is 360 degrees. So,
[tex]m(arc(AD))+m(arc(BC))+m(arc(CD))+m(arc(AB))=360^\circ[/tex]
[tex]105^\circ+35^\circ+50^\circ+m(arc(AB))=360^\circ[/tex]
[tex]190^\circ+m(arc(AB))=360^\circ[/tex]
[tex]m(arc(AB))=360^\circ-190^\circ[/tex]
[tex]m(arc(AB))=170^\circ[/tex]
Therefore, the measure of arc AD is 105°, the measure of arc BC is 35°, the measure of arc CD is 50° and the measure of arc AB is 170°
