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°

74°
74°

53°
53°

Answer 1

To find the arc measure of MN in the given triangle LMN, where angle L measures 37°, we can use the property of inscribed angles. An inscribed angle is half of the measure of the arc that subtends it.

In this case, since angle L is inscribed and subtends the arc MN, we can express the relationship as follows:

\[ \text{Measure of arc MN} = 2 \times \text{measure of angle L} \]

Given that the measure of angle L is 37°:

\[ \text{Measure of arc MN} = 2 \times 37° = 74° \]

Thus, the arc measure of MN is 74°.