Triangle LMN

Question

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°

106°
106°

53°
53°

74°

Answer 1

In a circle, an inscribed angle is half the measure of the arc that it subtends. In this case, the triangle LMN is inscribed in the circle with LM as the diameter, and angle L (at vertex L) measures 37°.

Since angle L is inscribed and subtends arc MN, we can calculate the measure of arc MN as follows:

\[ \text{Arc measure of } MN = 2 \times \text{inscribed angle at L} \]

Substituting the value we have:

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

Therefore, the arc measure of MN is 74°.