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 .

Answer 1

Since triangle LMN is inscribed inside the circle with diameter LM, angle N is an inscribed angle. By the inscribed angle theorem, the measure of angle N is equal to half the measure of the arc MN.

Given that the measure of angle L is 37°, the measure of angle N is 37° as well. Therefore, the arc measure of MN is twice the measure of angle N, which is 2 * 37° = 74°.

Thus, the arc measure of MN is 74°.