Triangle LMN is inscribed inside a circle with diameter LM; the inscribed angle is N. The angle measure at the vertex L is 37°. Using what you understand about inscribed angles, find the arc measure of MN.(1 point)Responses74°74°106°106°90°90°53°53°

Answer 1

In a circle, the inscribed angle theorem states that an inscribed angle is half the measure of the arc it intercepts. In this case, triangle LMN has its angle at vertex L measuring \(37^\circ\). The inscribed angle at L intercepts the arc MN.

To find the measure of the arc MN, we can use the relationship:

\[ \text{Measure of arc MN} = 2 \times \text{measure of angle L} \]

Substituting the given value:

\[ \text{Measure of arc MN} = 2 \times 37^\circ = 74^\circ \]

Thus, the arc measure of MN is:

\[ \boxed{74^\circ} \]