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)

Answer 1

In a circle, the inscribed angle intercepts an arc that is twice its measure. Given that triangle LMN is inscribed in a circle with diameter LM, and the angle at vertex L (angle \( L \)) measures 37°, we can find the measure of the arc MN.

In this case, angle \( L \) is the inscribed angle that intercepts arc \( MN \). According to the inscribed angle theorem, the measure of arc \( MN \) is twice the measure of angle \( L \).

So, we calculate:

\[ \text{Arc } MN = 2 \times \text{measure of angle } L = 2 \times 37° = 74°. \]

Therefore, the arc measure of MN is \( 74° \).