Help me please

Dear Student,

10. Angle subtended at center = Twice the angle subtended on any point on the arc
$\angle NAI = 2\angle L \Rightarrow \angle L = \frac{30°}{2}=15°$
So, option A is the correct answer.

11. $\angle L$ and $\angle NEI$ are in the same segment. So they have equal measures. 

So, option A is the correct answer.

12.  Angle subtended at center = Twice the angle subtended on any point on the arc
$\angle HAN = 2\angle HEN \Rightarrow \angle HEN = \frac{120°}{2} = 60°$

So option B is the correct answer.

13. Since NL is a diameter, and Angle subtended at center = Twice the angle subtended on any point on the arc, 
$\angle NEL = \frac{180°}{2}=90°$
So the measure of arc NEL will be 180 degrees.

So option A is the correct answer.

14. Angle subtended at center = Twice the angle subtended on any point on the arc
$\angle LAE = 2\angle N \Rightarrow \angle LAE = 40°$
$$\begin{gathered} \angle HAL = 180° - 120° = 60° \\ \angle HAE = \angle HAL + \angle LAE = 60° + 40° = 100° \end{gathered}$$

Angle subtended at center = Twice the angle subtended on any point on the arc
$\angle HNE = \angle HAE/2 = 50°$
Opposite angles of cyclic quadrilateral HLEN are supplementary
$\angle HLE = 180° - \angle HNE = 130°$

So none of the given options is the right answer.

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