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) Responses 106° 106° 74° 74° 53° 53° 90°

Answer 1

In a circle, inscribed angles that subtend the same arc are equal. Additionally, an inscribed angle is half the measure of the arc it intercepts.

In triangle LMN, since angle N is the inscribed angle, it intercepts the arc MN. We know that the diameter LM subtends a semicircle, which means that the arc LM measures 180°.

The angle at vertex L is given as 37°. This angle subtends arc MN (the arc opposite angle L). According to the inscribed angle theorem, we can find the measure of arc MN:

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

Substituting the value of angle L:

\[ \text{measure of arc MN} = 2 \times 37° = 74° \]

Therefore, the measure of arc MN is 74°.