What is the value of angle x rounded to the nearest whole number

  x ≈ 42°

Step-by-step explanation:

Label the vertices of the quadrilateral shown at the upper left in you diagram A, B, C, and D, starting at the lower left. Label the center point X. Then the red line is CX and the lower two line segments are CD and DA. (A, C, D, and X are not coplanar.)

Angle D of triangle ACD is the interior angle of a regular pentagon, so measures 108°. That means angle ACD measures (180° -108°)/2 = 36°. If we label the midpoint of segment AC point Y, then the length of segment CY is ...

  CY = CD·cos(36°)

Now triangle BCD is an equilateral triangle, so segment CX will have a length corresponding to the altitude of that triangle, CD·√3/2. Shifting our focus to the triangle AXC, we find that angle XCY will satisfy the relation ...

  cos(XCY) = CY/CX = CD·cos(36°)/(CD·√3/2) = (2/)√3·cos(36°)

Angle x is the exterior angle of triangle AXC that is opposite the two equal interior angles XCY and XAY. Hence its value is double that of angle XCY.

  angle x = 2·arccos((2/√3)·cos(36°)) ≈ 2·20.905° ≈ 41.81°

  angle x ≈ 42°

Comment on the angle

The icosahedron is the only Platonic solid with a dihedral angle more than 120°. It is about 138.19°, the supplement to angle x.

Comment on point labels

It may help to label the points in the 3-d version of the figure. Then you can see that segment AC is a line through the interior space of the icosahedron.

answer: f = 32.2m

step-by-step explanation: that is the answer

"it's not the heat, it's the humidity".   that's a partly valid phrase you may have heard in the summer, but it's actually both.   the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature.   this has important considerations for the human body's comfort.   when the body gets too hot, it begins to perspire or sweat to cool itself off.   if the perspiration is not able to evaporate, the body cannot regulate its temperature.   evaporation is a cooling process.   when perspiration is evaporated off the body, it effectively reduces the body's temperature.   when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases.   in other words, the human body feels warmer in humid conditions.   the opposite is true when the relative humidity decreases because the rate of perspiration increases.   the body actually feels cooler in arid conditions.   there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

step-by-step explanation: