Question

Can someone please help me solve this

Answer 1

Answer:

$m\angle1=75^{\circ}$

Step-by-step explanation:

Solution 1:

$m\angle1$ is formed by a point that is on the circle. The angle encompasses an arc of $150^{\circ}$ and thus the measure of the angle formed is $\frac{150}{2}=\fbox{ 75^{\circ} }$.

Solution 2:

Since $\angle 1$ is adjacent to a line and encompasses an arc, we can set up the following proportion:

$\frac{150}{360}=\frac{m\angle 1}{180}$

Solving, we get $m\angle 1=\fbox{ 75^{\circ} }$.