Answer:
[tex]m\angle1=75^{\circ}[/tex]
Step-by-step explanation:
Solution 1:
[tex]m\angle1[/tex] is formed by a point that is on the circle. The angle encompasses an arc of [tex]150^{\circ}[/tex] and thus the measure of the angle formed is [tex]\frac{150}{2}=\fbox{$75^{\circ}$}[/tex].
Solution 2:
Since [tex]\angle 1[/tex] is adjacent to a line and encompasses an arc, we can set up the following proportion:
[tex]\frac{150}{360}=\frac{m\angle 1}{180}[/tex]
Solving, we get [tex]m\angle 1=\fbox{$75^{\circ}$}[/tex].
