a lawn is watered by a sprinkler that has two fixed spray heads that each spray water in a fan shape. The angle that determines each of the fan shapes is 120 degrees. The two fans shapes overlap at <2. m<1 is 30 degress and m<3 is 30 degress . What is m<2
To find the measure of angle m<2, we need to use the fact that the two fans overlap at angle m<1 and angle m<3.
Let's start by visualizing the situation. Draw a diagram of the two fans with their spray heads, overlapping at their ends. Label the angles accordingly:
Fan 1
_______ 30° _______
/ \
m<1 m<2
\________ 30° _______/
Fan 2
From the diagram, we can see that angle m<2 is the remaining angle between the two fans.
To find the measure of angle m<2, we can use the information that the spray heads have a fan shape angle of 120 degrees.
Since angle m<1 and angle m<3 each have a measure of 30 degrees, we can calculate the measure of angle m<2:
m<2 = Total angle of spray fan - (m<1 + m<3)
m<2 = 120° - (30° + 30°)
m<2 = 120° - 60°
m<2 = 60°
Therefore, the measure of angle m<2 is 60 degrees.