The line GH bisects The triangle FGI meaning it divides it into two equal parts <em>(that is the definition if bisection); </em>therefore, the angles FGH and HGI are equal:
Now let us add 2 to both sides gives
subtracting 4x from both sides gives
Hence, x = 11.
The measure of FGH is
(B)
The measure of HGI is
(C)
The measure of FGI is the sum of HGI and FGH:
<em />
The approximate area that is within range of the motion sensor is 4975 square meters
<h3>How to determine the area of the range?</h3>The figure is not given, however the area of the range can be calculated without the figure.
The given parameters are:
Angle, ⊕ = 135°
Radius, r = 65 meters
The area of the range is calculated using the following sector area
This gives
Evaluate
A = 4974.9375
Approximate
A = 4975
Hence, the approximate area that is within range of the motion sensor is 4975 square meters
Read more about sector areas at:
#SPJ1