Question
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°
53°
53°
90°
90°
74°
74°
Responses
106°
106°
53°
53°
90°
90°
74°
74°
Answers
GPT-4o mini
In a circle, the inscribed angle is half the measure of the arc it intercepts. Here, we have triangle LMN inscribed in a circle with diameter LM and the angle at vertex L (which is inscribed angle N) measuring 37°.
Since angle L intercepts arc MN, we can find the measure of arc MN by using the relationship between an inscribed angle and the arc it intercepts:
\[
\text{Measure of arc MN} = 2 \times \text{Measure of angle L}
\]
Substituting the given value:
\[
\text{Measure of arc MN} = 2 \times 37° = 74°
\]
Therefore, the arc measure of MN is **74°**.
Since angle L intercepts arc MN, we can find the measure of arc MN by using the relationship between an inscribed angle and the arc it intercepts:
\[
\text{Measure of arc MN} = 2 \times \text{Measure of angle L}
\]
Substituting the given value:
\[
\text{Measure of arc MN} = 2 \times 37° = 74°
\]
Therefore, the arc measure of MN is **74°**.