Question

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

90°
90°

74°
74°

53°
53°

106°

Answer 1

To solve for the arc measure of \( MN \), we can use the properties of inscribed angles.

Given that triangle \( LMN \) is inscribed in a circle with diameter \( LM \), and the angle at vertex \( L \) (which is the inscribed angle) measures \( 37^\circ \):

1. The inscribed angle \( \angle L \) intercepts the arc \( MN \).
2. The measure of an inscribed angle is half the measure of the arc it intercepts.

Thus, we can set up the equation:

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

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

The correct response is:

**74°**